Find the Inverse 96000+80x

$96000 + 80 x$

Step 1

Interchange the variables.

$x = 96000 + 80 y$

Step 2

Solve for $y$ .

Rewrite the equation as $96000 + 80 y = x$ .

$96000 + 80 y = x$

Subtract $96000$ from both sides of the equation.

$80 y = x - 96000$

Divide each term in $80 y = x - 96000$ by $80$ and simplify.

Divide each term in $80 y = x - 96000$ by $80$ .

$\frac{80 y}{80} = \frac{x}{80} + \frac{- 96000}{80}$

Simplify the left side.

Cancel the common factor of $80$ .

Cancel the common factor.

$\frac{80 y}{80} = \frac{x}{80} + \frac{- 96000}{80}$

Divide $y$ by $1$ .

$y = \frac{x}{80} + \frac{- 96000}{80}$

Simplify the right side.

Divide $- 96000$ by $80$ .

$y = \frac{x}{80} - 1200$

Step 3

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

$f^{- 1} (x) = \frac{x}{80} - 1200$

Step 4

Verify if $f^{- 1} (x) = \frac{x}{80} - 1200$ is the inverse of $f (x) = 96000 + 80 x$ .

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 $f^{- 1} (96000 + 80 x)$ by substituting in the value of $f$ into $f^{- 1}$ .

$f^{- 1} (96000 + 80 x) = \frac{96000 + 80 x}{80} - 1200$

Cancel the common factor of $96000 + 80 x$ and $80$ .

Factor $80$ out of $96000$ .

$f^{- 1} (96000 + 80 x) = \frac{80 \cdot 1200 + 80 x}{80} - 1200$

Factor $80$ out of $80 x$ .

$f^{- 1} (96000 + 80 x) = \frac{80 \cdot 1200 + 80 (x)}{80} - 1200$

Factor $80$ out of $80 (1200) + 80 (x)$ .

$f^{- 1} (96000 + 80 x) = \frac{80 (1200 + x)}{80} - 1200$

Cancel the common factors.

Factor $80$ out of $80$ .

$f^{- 1} (96000 + 80 x) = \frac{80 (1200 + x)}{80 (1)} - 1200$

Cancel the common factor.

$f^{- 1} (96000 + 80 x) = \frac{80 (1200 + x)}{80 \cdot 1} - 1200$

Rewrite the expression.

$f^{- 1} (96000 + 80 x) = \frac{1200 + x}{1} - 1200$

Divide $1200 + x$ by $1$ .

$f^{- 1} (96000 + 80 x) = 1200 + x - 1200$

Combine the opposite terms in $1200 + x - 1200$ .

Subtract $1200$ from $1200$ .

$f^{- 1} (96000 + 80 x) = x + 0$

Add $x$ and $0$ .

$f^{- 1} (96000 + 80 x) = x$

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

Set up the composite result function.

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

Evaluate $f (\frac{x}{80} - 1200)$ by substituting in the value of $f^{- 1}$ into $f$ .

$f (\frac{x}{80} - 1200) = 96000 + 80 (\frac{x}{80} - 1200)$

Simplify each term.

Apply the distributive property.

$f (\frac{x}{80} - 1200) = 96000 + 80 (\frac{x}{80}) + 80 \cdot - 1200$

Cancel the common factor of $80$ .

Cancel the common factor.

$f (\frac{x}{80} - 1200) = 96000 + 80 (\frac{x}{80}) + 80 \cdot - 1200$

Rewrite the expression.

$f (\frac{x}{80} - 1200) = 96000 + x + 80 \cdot - 1200$

Multiply $80$ by $- 1200$ .

$f (\frac{x}{80} - 1200) = 96000 + x - 96000$

Combine the opposite terms in $96000 + x - 96000$ .

Subtract $96000$ from $96000$ .

$f (\frac{x}{80} - 1200) = x + 0$

Add $x$ and $0$ .

$f (\frac{x}{80} - 1200) = x$

Since $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ , then $f^{- 1} (x) = \frac{x}{80} - 1200$ is the inverse of $f (x) = 96000 + 80 x$ .

$f^{- 1} (x) = \frac{x}{80} - 1200$

Find the Inverse 96000+80x

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