Find the inverse of the following function of f (x) = 3 square root x+12

f^ (-1) (x) = x^3-2

Step-by-step explanation:

f (x) = ∛ (x+2)

To find the inverse,

Let

y = ∛ (x+2)

Replacing x with y and y with x

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

Solving for y

x^3=[ (y+2) ^ (1/3) ]^3

x^3=y+2

y=x^3-2

Finally replacing y with f-1 (x)

f^ (-1) (x) = x^3-2

f^-1 (x) = x³ - 12

got this one right