Question

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

Answer 1

Answer:

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

Answer 2

Answer:

g(x) = 1/4 x -3

Step-by-step 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