Answer:
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.