Question

If g(x) is the inverse of f(x) and S(x) = 4x+12, what is g(x)?
g(x) = 12x + 4
g(x) = 4x12
g(x) = x= 3
8(t) = 1x-3

Answer 1

Answer:

$g(x)=\frac{1}{4}x-3$

Step-by-step explanation:

we have

$f(x)=4x+12$

Find the inverse

step 1

Let

y=f(x)

$y=4x+12$

step 2

Exchange the variables  (x for y and y for x)

$x=4y+12$

step 3

Isolate the variable y

we have

$x=4y+12$

Subtract 12 both sides

$x-12=4y$

Divide by 4 both sides

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

simplify

$y=\frac{1}{4}x-3$

step 4

Let

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

$f^{-1}(x)=\frac{1}{4}x-3$

we have that

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

therefore

$g(x)=\frac{1}{4}x-3$