Find the Inverse f(x)=( cube root of x-7)/5

$f (x) = \frac{\sqrt[3]{x} - 7}{5}$

Step 1

Write $f (x) = \frac{\sqrt[3]{x} - 7}{5}$ as an equation.

$y = \frac{\sqrt[3]{x} - 7}{5}$

Step 2

Interchange the variables.

$x = \frac{\sqrt[3]{y} - 7}{5}$

Step 3

Solve for $y$ .

Rewrite the equation as $\frac{\sqrt[3]{y} - 7}{5} = x$ .

$\frac{\sqrt[3]{y} - 7}{5} = x$

Multiply both sides of the equation by $5$ .

$5 \frac{\sqrt[3]{y} - 7}{5} = 5 x$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$5 \frac{\sqrt[3]{y} - 7}{5} = 5 x$

Rewrite the expression.

$\sqrt[3]{y} - 7 = 5 x$

Add $7$ to both sides of the equation.

$\sqrt[3]{y} = 5 x + 7$

To remove the radical on the left side of the equation, cube both sides of the equation.

${\sqrt[3]{y}}^{3} = {(5 x + 7)}^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{y}$ as $y^{\frac{1}{3}}$ .

${(y^{\frac{1}{3}})}^{3} = {(5 x + 7)}^{3}$

Simplify the left side.

Simplify ${(y^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${(y^{\frac{1}{3}})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$y^{\frac{1}{3} \cdot 3} = {(5 x + 7)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$y^{\frac{1}{3} \cdot 3} = {(5 x + 7)}^{3}$

Rewrite the expression.

$y^{1} = {(5 x + 7)}^{3}$

Simplify.

$y = {(5 x + 7)}^{3}$

Simplify the right side.

Simplify ${(5 x + 7)}^{3}$ .

Use the Binomial Theorem.

$y = {(5 x)}^{3} + 3 {(5 x)}^{2} \cdot 7 + 3 (5 x) \cdot 7^{2} + 7^{3}$

Simplify each term.

Apply the product rule to $5 x$ .

$y = 5^{3} x^{3} + 3 {(5 x)}^{2} \cdot 7 + 3 (5 x) \cdot 7^{2} + 7^{3}$

Raise $5$ to the power of $3$ .

$y = 125 x^{3} + 3 {(5 x)}^{2} \cdot 7 + 3 (5 x) \cdot 7^{2} + 7^{3}$

Apply the product rule to $5 x$ .

$y = 125 x^{3} + 3 (5^{2} x^{2}) \cdot 7 + 3 (5 x) \cdot 7^{2} + 7^{3}$

Raise $5$ to the power of $2$ .

$y = 125 x^{3} + 3 (25 x^{2}) \cdot 7 + 3 (5 x) \cdot 7^{2} + 7^{3}$

Multiply $25$ by $3$ .

$y = 125 x^{3} + 75 x^{2} \cdot 7 + 3 (5 x) \cdot 7^{2} + 7^{3}$

Multiply $7$ by $75$ .

$y = 125 x^{3} + 525 x^{2} + 3 (5 x) \cdot 7^{2} + 7^{3}$

Multiply $5$ by $3$ .

$y = 125 x^{3} + 525 x^{2} + 15 x \cdot 7^{2} + 7^{3}$

Raise $7$ to the power of $2$ .

$y = 125 x^{3} + 525 x^{2} + 15 x \cdot 49 + 7^{3}$

Multiply $49$ by $15$ .

$y = 125 x^{3} + 525 x^{2} + 735 x + 7^{3}$

Raise $7$ to the power of $3$ .

$y = 125 x^{3} + 525 x^{2} + 735 x + 343$

Step 4

Replace $y$ with $f^{- 1} (x)$ to show the final answer.

$f^{- 1} (x) = 125 x^{3} + 525 x^{2} + 735 x + 343$

Step 5

Verify if $f^{- 1} (x) = 125 x^{3} + 525 x^{2} + 735 x + 343$ is the inverse of $f (x) = \frac{\sqrt[3]{x} - 7}{5}$ .

To verify the inverse, check if $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ .

Evaluate $f^{- 1} (f (x))$ .

Set up the composite result function.

$f^{- 1} (f (x))$

Evaluate $f^{- 1} (\frac{\sqrt[3]{x} - 7}{5})$ by substituting in the value of $f$ into $f^{- 1}$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = 125 {(\frac{\sqrt[3]{x} - 7}{5})}^{3} + 525 {(\frac{\sqrt[3]{x} - 7}{5})}^{2} + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Simplify each term.

Apply the product rule to $\frac{\sqrt[3]{x} - 7}{5}$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = 125 (\frac{{(\sqrt[3]{x} - 7)}^{3}}{5^{3}}) + 525 {(\frac{\sqrt[3]{x} - 7}{5})}^{2} + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Raise $5$ to the power of $3$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = 125 (\frac{{(\sqrt[3]{x} - 7)}^{3}}{125}) + 525 {(\frac{\sqrt[3]{x} - 7}{5})}^{2} + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Cancel the common factor of $125$ .

Cancel the common factor.

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = 125 (\frac{{(\sqrt[3]{x} - 7)}^{3}}{125}) + 525 {(\frac{\sqrt[3]{x} - 7}{5})}^{2} + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Rewrite the expression.

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = {(\sqrt[3]{x} - 7)}^{3} + 525 {(\frac{\sqrt[3]{x} - 7}{5})}^{2} + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Use the Binomial Theorem.

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = {\sqrt[3]{x}}^{3} + 3 {\sqrt[3]{x}}^{2} \cdot - 7 + 3 \sqrt[3]{x} {(- 7)}^{2} + {(- 7)}^{3} + 525 {(\frac{\sqrt[3]{x} - 7}{5})}^{2} + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Simplify each term.

Rewrite ${\sqrt[3]{x}}^{3}$ as $x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x}$ as $x^{\frac{1}{3}}$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = {(x^{\frac{1}{3}})}^{3} + 3 {\sqrt[3]{x}}^{2} \cdot - 7 + 3 \sqrt[3]{x} {(- 7)}^{2} + {(- 7)}^{3} + 525 {(\frac{\sqrt[3]{x} - 7}{5})}^{2} + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x^{\frac{1}{3} \cdot 3} + 3 {\sqrt[3]{x}}^{2} \cdot - 7 + 3 \sqrt[3]{x} {(- 7)}^{2} + {(- 7)}^{3} + 525 {(\frac{\sqrt[3]{x} - 7}{5})}^{2} + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Combine $\frac{1}{3}$ and $3$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x^{\frac{3}{3}} + 3 {\sqrt[3]{x}}^{2} \cdot - 7 + 3 \sqrt[3]{x} {(- 7)}^{2} + {(- 7)}^{3} + 525 {(\frac{\sqrt[3]{x} - 7}{5})}^{2} + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Cancel the common factor of $3$ .

Cancel the common factor.

Rewrite the expression.

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x + 3 {\sqrt[3]{x}}^{2} \cdot - 7 + 3 \sqrt[3]{x} {(- 7)}^{2} + {(- 7)}^{3} + 525 {(\frac{\sqrt[3]{x} - 7}{5})}^{2} + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Simplify.

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x + 3 {\sqrt[3]{x}}^{2} \cdot - 7 + 3 \sqrt[3]{x} {(- 7)}^{2} + {(- 7)}^{3} + 525 {(\frac{\sqrt[3]{x} - 7}{5})}^{2} + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Rewrite ${\sqrt[3]{x}}^{2}$ as ${(x^{2})}^{\frac{1}{3}}$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x + 3 \sqrt[3]{x^{2}} \cdot - 7 + 3 \sqrt[3]{x} {(- 7)}^{2} + {(- 7)}^{3} + 525 {(\frac{\sqrt[3]{x} - 7}{5})}^{2} + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Multiply $- 7$ by $3$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 3 \sqrt[3]{x} {(- 7)}^{2} + {(- 7)}^{3} + 525 {(\frac{\sqrt[3]{x} - 7}{5})}^{2} + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Raise $- 7$ to the power of $2$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 3 \sqrt[3]{x} \cdot 49 + {(- 7)}^{3} + 525 {(\frac{\sqrt[3]{x} - 7}{5})}^{2} + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Multiply $49$ by $3$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} + {(- 7)}^{3} + 525 {(\frac{\sqrt[3]{x} - 7}{5})}^{2} + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Raise $- 7$ to the power of $3$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 525 {(\frac{\sqrt[3]{x} - 7}{5})}^{2} + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Apply the product rule to $\frac{\sqrt[3]{x} - 7}{5}$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 525 (\frac{{(\sqrt[3]{x} - 7)}^{2}}{5^{2}}) + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Raise $5$ to the power of $2$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 525 (\frac{{(\sqrt[3]{x} - 7)}^{2}}{25}) + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Cancel the common factor of $25$ .

Factor $25$ out of $525$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 25 (21) (\frac{{(\sqrt[3]{x} - 7)}^{2}}{25}) + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Cancel the common factor.

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 25 \cdot (21 (\frac{{(\sqrt[3]{x} - 7)}^{2}}{25})) + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Rewrite the expression.

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 {(\sqrt[3]{x} - 7)}^{2} + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Rewrite ${(\sqrt[3]{x} - 7)}^{2}$ as $(\sqrt[3]{x} - 7) (\sqrt[3]{x} - 7)$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 ((\sqrt[3]{x} - 7) (\sqrt[3]{x} - 7)) + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Expand $(\sqrt[3]{x} - 7) (\sqrt[3]{x} - 7)$ using the FOIL Method.

Apply the distributive property.

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 (\sqrt[3]{x} (\sqrt[3]{x} - 7) - 7 (\sqrt[3]{x} - 7)) + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Apply the distributive property.

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 (\sqrt[3]{x} \sqrt[3]{x} + \sqrt[3]{x} \cdot - 7 - 7 (\sqrt[3]{x} - 7)) + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Apply the distributive property.

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 (\sqrt[3]{x} \sqrt[3]{x} + \sqrt[3]{x} \cdot - 7 - 7 \sqrt[3]{x} - 7 \cdot - 7) + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Simplify and combine like terms.

Simplify each term.

Multiply $\sqrt[3]{x} \sqrt[3]{x}$ .

Raise $\sqrt[3]{x}$ to the power of $1$ .

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 ({\sqrt[3]{x}}^{1 + 1} + \sqrt[3]{x} \cdot - 7 - 7 \sqrt[3]{x} - 7 \cdot - 7) + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Add $1$ and $1$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 ({\sqrt[3]{x}}^{2} + \sqrt[3]{x} \cdot - 7 - 7 \sqrt[3]{x} - 7 \cdot - 7) + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Rewrite ${\sqrt[3]{x}}^{2}$ as ${(x^{2})}^{\frac{1}{3}}$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 (\sqrt[3]{x^{2}} + \sqrt[3]{x} \cdot - 7 - 7 \sqrt[3]{x} - 7 \cdot - 7) + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Move $- 7$ to the left of $\sqrt[3]{x}$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 (\sqrt[3]{x^{2}} - 7 \cdot \sqrt[3]{x} - 7 \sqrt[3]{x} - 7 \cdot - 7) + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Multiply $- 7$ by $- 7$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 (\sqrt[3]{x^{2}} - 7 \sqrt[3]{x} - 7 \sqrt[3]{x} + 49) + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Subtract $7 \sqrt[3]{x}$ from $- 7 \sqrt[3]{x}$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 (\sqrt[3]{x^{2}} - 14 \sqrt[3]{x} + 49) + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Apply the distributive property.

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 \sqrt[3]{x^{2}} + 21 (- 14 \sqrt[3]{x}) + 21 \cdot 49 + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Simplify.

Multiply $- 14$ by $21$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 \sqrt[3]{x^{2}} - 294 \sqrt[3]{x} + 21 \cdot 49 + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Multiply $21$ by $49$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 \sqrt[3]{x^{2}} - 294 \sqrt[3]{x} + 1029 + 735 (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Cancel the common factor of $5$ .

Factor $5$ out of $735$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 \sqrt[3]{x^{2}} - 294 \sqrt[3]{x} + 1029 + 5 (147) (\frac{\sqrt[3]{x} - 7}{5}) + 343$

Cancel the common factor.

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 \sqrt[3]{x^{2}} - 294 \sqrt[3]{x} + 1029 + 5 \cdot (147 (\frac{\sqrt[3]{x} - 7}{5})) + 343$

Rewrite the expression.

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 \sqrt[3]{x^{2}} - 294 \sqrt[3]{x} + 1029 + 147 (\sqrt[3]{x} - 7) + 343$

Apply the distributive property.

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 \sqrt[3]{x^{2}} - 294 \sqrt[3]{x} + 1029 + 147 \sqrt[3]{x} + 147 \cdot - 7 + 343$

Multiply $147$ by $- 7$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 \sqrt[3]{x^{2}} - 294 \sqrt[3]{x} + 1029 + 147 \sqrt[3]{x} - 1029 + 343$

Simplify by adding terms.

Combine the opposite terms in $x - 21 \sqrt[3]{x^{2}} + 147 \sqrt[3]{x} - 343 + 21 \sqrt[3]{x^{2}} - 294 \sqrt[3]{x} + 1029 + 147 \sqrt[3]{x} - 1029 + 343$ .

Add $- 21 \sqrt[3]{x^{2}}$ and $21 \sqrt[3]{x^{2}}$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x + 0 + 147 \sqrt[3]{x} - 343 - 294 \sqrt[3]{x} + 1029 + 147 \sqrt[3]{x} - 1029 + 343$

Add $x$ and $0$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x + 147 \sqrt[3]{x} - 343 - 294 \sqrt[3]{x} + 1029 + 147 \sqrt[3]{x} - 1029 + 343$

Subtract $1029$ from $1029$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x + 147 \sqrt[3]{x} - 343 - 294 \sqrt[3]{x} + 0 + 147 \sqrt[3]{x} + 343$

Add $x + 147 \sqrt[3]{x} - 343 - 294 \sqrt[3]{x}$ and $0$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x + 147 \sqrt[3]{x} - 343 - 294 \sqrt[3]{x} + 147 \sqrt[3]{x} + 343$

Add $- 343$ and $343$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x + 147 \sqrt[3]{x} + 0 - 294 \sqrt[3]{x} + 147 \sqrt[3]{x}$

Add $x + 147 \sqrt[3]{x}$ and $0$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x + 147 \sqrt[3]{x} - 294 \sqrt[3]{x} + 147 \sqrt[3]{x}$

Subtract $294 \sqrt[3]{x}$ from $147 \sqrt[3]{x}$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x - 147 \sqrt[3]{x} + 147 \sqrt[3]{x}$

Combine the opposite terms in $x - 147 \sqrt[3]{x} + 147 \sqrt[3]{x}$ .

Add $- 147 \sqrt[3]{x}$ and $147 \sqrt[3]{x}$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x + 0$

Add $x$ and $0$ .

$f^{- 1} (\frac{\sqrt[3]{x} - 7}{5}) = x$

Evaluate $f (f^{- 1} (x))$ .

Set up the composite result function.

$f (f^{- 1} (x))$

Evaluate $f (125 x^{3} + 525 x^{2} + 735 x + 343)$ by substituting in the value of $f^{- 1}$ into $f$ .

$f (125 x^{3} + 525 x^{2} + 735 x + 343) = \frac{\sqrt[3]{125 x^{3} + 525 x^{2} + 735 x + 343} - 7}{5}$

Since $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ , then $f^{- 1} (x) = 125 x^{3} + 525 x^{2} + 735 x + 343$ is the inverse of $f (x) = \frac{\sqrt[3]{x} - 7}{5}$ .

$f^{- 1} (x) = 125 x^{3} + 525 x^{2} + 735 x + 343$

Find the Inverse f(x)=( cube root of x-7)/5

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