Question

Given the function f(x) = 6(x+2) − 3, solve for the inverse function when x = 21.

Answer 1

f⁻¹(21) = 2

Explanation:

Answer 2

f(x) = 6(x +2) - 3

let y = f(x)

y = 6x + 12 - 3

y = 6x + 9 solving for x.

y - 9 = 6x

6x = y - 9

x = (y - 9)/6

Recall f(x) = y. Implies x = f⁻¹(y)

x = (y - 9)/6

f⁻¹(y) = (y - 9)/6

So as well:

f⁻¹(x) = (x - 9)/6 when x = 21

f⁻¹(21) = (21 - 9)/6 = 12/6 = 2

f⁻¹(21) = 2