For the function f(x)=(x+10)^1/3
find f^-1(x)
To find the inverse function f^⁻1(x) for f(x) = (x+10)^(1/3), we can follow these steps:
Step 1: Replace f(x) with y.
y = (x+10)^(1/3)
Step 2: Swap x and y.
x = (y+10)^(1/3)
Step 3: Solve for y.
To get rid of the cube root, cube both sides.
x^3 = y+10
Step 4: Solve for y.
Subtract 10 from both sides.
y = x^3 - 10
Therefore, the inverse function of f(x) = (x+10)^(1/3) is f^⁻1(x) = x^3 - 10.