Question

If g(7) is the inverse of x) and x) = 4x+ 12. what is glx)?

Answer 1

Question:

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

Answer:

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

Explanation:

Given

`f(x) = 4x + 12`

Required

Find g(x)

`f(x) = 4x + 12`

Replace f(x) with y

`y = 4x + 12`

Swap the positions of y and x

`x = 4y + 12`

Make y the subject: Subtract 12 from both sides

`x -12= 4y + 12-12`

`x -12= 4y`

Make y the subject: Divide through by 3

`(x)/(4) -(12)/(4)= (4y )/(4)`

`(x)/(4) -(12)/(4)= y`

`y = (x)/(4) -(12)/(4)`

Since g(x) is the inverse, replace y with g(x)

`g(x) = (x)/(4) -(12)/(4)`

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