Question

Let f(x)=(x-2)^3+8 Find the inverse of f(x). Please show steps in written form would be gladly appreciated

Answer 1

Hello from MrBillDoesMath!

Answer:

(x-8)^(1/3) +2

Discussion:

To find the inverse of a function swap the values of x and y in the original equation y = (x-2)^3 +8 and solve for y.

y = (x-2)^3 +8 => original function. swap x and y values

x = (y-2)^3 + 8 => subtract 8 from both sides

x - 8 = (y -2)^3 => take cube root of both sides

(x-8)^(1/3) = y - 2 => add 2 to both sides

(x-8)^(1/3) +2 = y => y is the inverse

Thank you,

MrB