Question

The function f(x)=x³-8 is one-to-one. Find an equation for f⁻ˣ, the inverse function.

Answer 1

To find the inverse function of f(x) = x³-8, swap the x and y variables and solve for y. The inverse function is f⁻¹(x) = ∛(x + 8).

Step-by-step explanation:

To find the inverse function of f(x) = x³-8, we need to swap the x and y variables and solve for y.

Step 1: Write the function equation as
y = x³-8

Step 2: Swap the x and y variables
x = y³-8

Step 3: Solve for y by adding 8 and taking the cube root of both sides
x + 8 = y³
y = ∛(x + 8)

Therefore, the inverse function of f(x) = x³-8 is f⁻¹(x) = ∛(x + 8).