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:

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

Step-by-step 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

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

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

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

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

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

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