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

`g(x)=(1)/(4)x-3`

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=(x-12)/(4)`

simplify

`y=(1)/(4)x-3`

step 4

Let

`f^(-1)(x)=y`

`f^(-1)(x)=(1)/(4)x-3`

we have that

`g(x)=f^(-1)(x)`

therefore

`g(x)=(1)/(4)x-3`