Question

Find the inverse of the following function.

f(x) = 3squareroot x + 12

Answer 1

f(x) = 3 · √x + 12

Let f(x) = y

y = 3 · √x + 12

y - 12 = 3 · √x .............. (Subtract 12 from both sides)

(y - 12)/3 = √x .............. (Divide both sides by 3)

(y/3) - (12/3) = √x

(y/3) - 4 = √x

[(y/3) - 4]² = x ............... (Square both sides)

Therefore, f⁻¹(y) = [(y/3) - 4]²

f⁻¹(x) = [(x/3) - 4]²