Find the inverse of each of the given functions.

Do:s

Ask by Wagner Matthews. in the United States

Dec 16,2024

Question

Find the inverse of each of the given functions. $$ f(x)=4 x-12 $$ $$ f^{-1}(x)=\square $$ Do:s $$ = $$

UpStudy AI · Accepted Answer

Find the inverse of the function $$ f(x)=4x-12 $$
Function by following steps:
- step0: Find the inverse:
  $$f\left(x\right)=4x-12$$
- step1: Replace $$f\left(x\right)$$ with $$y:$$
  $$y=4x-12$$
- step2: Interchange the variables:
  $$x=4y-12$$
- step3: Swap the sides:
  $$4y-12=x$$
- step4: Move the constant to the right side:
  $$4y=x+12$$
- step5: Divide both sides:
  $$\frac{4y}{4}=\frac{x+12}{4}$$
- step6: Divide the numbers:
  $$y=\frac{x+12}{4}$$
- step7: Replace $$y$$ with $$f^{-1}\left(x\right):$$
  $$f^{-1}\left(x\right) = \frac{x+12}{4}$$
The inverse of the function $$ f(x)=4x-12 $$ is $$ f^{-1}(x) = \frac{x+12}{4} $$.
$$ f^{-1}(x) = \frac{x+12}{4} $$

Find the inverse of each of the given functions.

Do:s

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Find the inverse of each of the given functions. Do:s