Question

If g(x) is the inverse of f(x)=4x+12 and f(x)=, what is g(x)

Answer 1

Hello,
f(x)=y=4x+12

x=4y+12
==>4y=x-12
==>y=x/12- 3

g(x)=x/12 -3

Answer 2

Answer:

$f^{-1}(x)=g(x)=\frac{x-12}{4}$

Step-by-step explanation:

The problem tell us that $g(x)$ is the inverse of $f(x)$, where:

$f(x)=4x+12$

So, we need to find the inverse function of $f(x)$ in order to find $g(x)$

Let's find the inverse function using the following steps:

1. Replace  $f(x)$ with $y$:

$f(x)=y=4x+12$

2. Solve the equation for $x$:

$\frac{y-12}{4} =x$

3. Replace every $x$ with a $y$ and replace every $y$ with a $x$:

$y=\frac{x-12}{4}$

4. Finally, replace $y$ with $f^{-1}(x)$

$f^{-1}(x)=\frac{x-12}{4}$

Therefore:

$g(x)=f^{-1}(x)=\frac{x-12}{4}$