Question

Find f^-1 for the function f(x)=(x-10)^3+4

Answer 1

f^(-1)(x)=(x-4)^(1/3)+10

Explanation:

So to find the inverse we need to first solve the equation y=(x-10)^3+4 for x.

Subtract 4 on both sides:

y-4=(x-10)^3

Cube root (or raise both sides to 1/3 power):

(y-4)^(1/3)=x-10

Add x on both sides:

(y-4)^(1/3)+10=x

Swap x and y:

(x-4)^(1/3)+10=y

Symmetric property of equality:

y=(x-4)^(1/3)+10

So f^(-1)(x)=(x-4)^(1/3)+10.