Find the Inverse 1/4x+2

$\frac{1}{4} x + 2$

Step 1

Interchange the variables.

$x = \frac{1}{4} y + 2$

Step 2

Solve for $y$ .

Rewrite the equation as $\frac{1}{4} y + 2 = x$ .

$\frac{1}{4} y + 2 = x$

Combine $\frac{1}{4}$ and $y$ .

$\frac{y}{4} + 2 = x$

Subtract $2$ from both sides of the equation.

$\frac{y}{4} = x - 2$

Multiply both sides of the equation by $4$ .

$4 \frac{y}{4} = 4 (x - 2)$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{y}{4} = 4 (x - 2)$

Rewrite the expression.

$y = 4 (x - 2)$

Simplify the right side.

Simplify $4 (x - 2)$ .

Apply the distributive property.

$y = 4 x + 4 \cdot - 2$

Multiply $4$ by $- 2$ .

$y = 4 x - 8$

Step 3

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

$f^{- 1} (x) = 4 x - 8$

Step 4

Verify if $f^{- 1} (x) = 4 x - 8$ is the inverse of $f (x) = \frac{1}{4} x + 2$ .

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 $f^{- 1} (\frac{1}{4} x + 2)$ by substituting in the value of $f$ into $f^{- 1}$ .

$f^{- 1} (\frac{1}{4} x + 2) = 4 (\frac{1}{4} x + 2) - 8$

Simplify each term.

Combine $\frac{1}{4}$ and $x$ .

$f^{- 1} (\frac{1}{4} x + 2) = 4 (\frac{x}{4} + 2) - 8$

Apply the distributive property.

$f^{- 1} (\frac{1}{4} x + 2) = 4 (\frac{x}{4}) + 4 \cdot 2 - 8$

Cancel the common factor of $4$ .

Cancel the common factor.

$f^{- 1} (\frac{1}{4} x + 2) = 4 (\frac{x}{4}) + 4 \cdot 2 - 8$

Rewrite the expression.

$f^{- 1} (\frac{1}{4} x + 2) = x + 4 \cdot 2 - 8$

Multiply $4$ by $2$ .

$f^{- 1} (\frac{1}{4} x + 2) = x + 8 - 8$

Combine the opposite terms in $x + 8 - 8$ .

Subtract $8$ from $8$ .

$f^{- 1} (\frac{1}{4} x + 2) = x + 0$

Add $x$ and $0$ .

$f^{- 1} (\frac{1}{4} x + 2) = x$

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

Set up the composite result function.

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

Evaluate $f (4 x - 8)$ by substituting in the value of $f^{- 1}$ into $f$ .

$f (4 x - 8) = \frac{1}{4} \cdot (4 x - 8) + 2$

Simplify each term.

Apply the distributive property.

$f (4 x - 8) = \frac{1}{4} \cdot (4 x) + \frac{1}{4} \cdot - 8 + 2$

Cancel the common factor of $4$ .

Factor $4$ out of $4 x$ .

$f (4 x - 8) = \frac{1}{4} \cdot (4 (x)) + \frac{1}{4} \cdot - 8 + 2$

Cancel the common factor.

$f (4 x - 8) = \frac{1}{4} \cdot (4 x) + \frac{1}{4} \cdot - 8 + 2$

Rewrite the expression.

$f (4 x - 8) = x + \frac{1}{4} \cdot - 8 + 2$

Cancel the common factor of $4$ .

Factor $4$ out of $- 8$ .

$f (4 x - 8) = x + \frac{1}{4} \cdot (4 (- 2)) + 2$

Cancel the common factor.

$f (4 x - 8) = x + \frac{1}{4} \cdot (4 \cdot - 2) + 2$

Rewrite the expression.

$f (4 x - 8) = x - 2 + 2$

Combine the opposite terms in $x - 2 + 2$ .

Add $- 2$ and $2$ .

$f (4 x - 8) = x + 0$

Add $x$ and $0$ .

$f (4 x - 8) = x$

Since $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ , then $f^{- 1} (x) = 4 x - 8$ is the inverse of $f (x) = \frac{1}{4} x + 2$ .

$f^{- 1} (x) = 4 x - 8$

Find the Inverse 1/4x+2

Related Questions

Support LCMGCF.com by disabling your adblocker.