Question

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

Answer 1

g(x) = 1/4 x -3

Explanation:

f (x) = 4 x + 12

g(x) = f⁻¹(x)

step 1: re-write as linear equation y = 4x+12

step 2: swap x and y x = 4y + 12

step 3: solve y 4y = x - 12 y = 1/4 x -3

step 4: inverse notation: f⁻¹(x) = 1/4 x - 3 i.e. g(x) = 1/4 x -3

Answer 2

`let \: the \: inverse \: of \: f(x) \: be \: m \\ m = {f(x)}^( - 1) \\ m = {(4x + 12)}^( - 1) \\ m = (1)/((4x + 12)) \\ m(4x + 12) = 1 \\ 4x = (1)/(m) - 12 \\ x = (1)/(4m) - 3 \\ therefore \\ g(x) = (1)/(4x) - 3`