Question

Find the inverse of the following function?

Answer 1

f(x) = (1/3)*x - 2

y = (1/3)*x - 2

x = (1/3)*y - 2

x+2 = (1/3)*y - 2+2

x+2 = (1/3)*y

(1/3)*y = x+2

3*(1/3)*y = 3(x+2)

y = 3(x+2)

y = 3x+6

Answer 2

Step 1) Replace f(x) with y
Step 2) Swap every copy of y with x (and vice versa)
Step 3) Solve for y

f(x) = (1/3)*x - 2
y = (1/3)*x - 2
x = (1/3)*y - 2
x+2 = (1/3)*y - 2+2
x+2 = (1/3)*y
(1/3)*y = x+2
3*(1/3)*y = 3*(x+2)
y = 3*(x+2)
y = 3x+6

The inverse function is therefore
`f^(-1)(x) = 3x+6`