Question

What is the inverse of the function f(x) = 3√(x¹²)?

1) f⁻¹(x) = x¹²
2) f⁻¹(x) = x³ - 12
3) f⁻¹(x) = 12 - x³
4) f⁻¹(x) = x - 12

Answer 1

The inverse of the function f(x) = 3√(x¹²) is f⁻¹(x) = x⁴.

Step-by-step explanation:

The inverse of the function f(x) = 3√(x¹²) is f⁻¹(x) = x⁴. In other words, to find the inverse of a function, we swap the roles of x and y and solve for y.

Step 1: Replace f(x) with y: y = 3√(x¹²)

Step 2: Swap x and y: x = 3√(y¹²)

Step 3: Solve for y: x = 3√(y¹²)

Step 4: Cube both sides to get rid of the square root: x³ = y¹²

Step 5: Take the ⁴√(x³) to find the inverse function: f⁻¹(x) = x⁴