Question

Given the function f(x) =5(x+4)-6 solve for the inverse function when x=19

Answer 1

f(x) = 5(x +4) - 6

let y = f(x)

y = 5x +20 - 6 solving for x.

y = 5x + 14

y - 14 = 5x

5x = y - 14

x = (y - 14)/5

Recall f(x) = y. Implies x = f⁻¹(y)

x = (y - 14)/5

f⁻¹(y) = (y - 14)/5

So as well:

f⁻¹(x) = (x - 14)/5 when x = 19

f⁻¹(19) = (19 - 14)/5 = 5/5

f⁻¹(19) = 1