Question

Which is the inverse of the function f(x)=4x^2 ?

Answer 1

for f(x) = 4x², x≥0, the inverse function is f⁻¹(x) = (1/2)√x

Explanation:

Solve for y:

x = f(y) = 4y^2

(x/4) = y^2

±√(x/4) = y = ±(1/2)√x

The domain of the original function must be restricted if it is to have an inverse. (The inverse relation cannot be double-valued if it is to be called an inverse function.) Usually we choose to restrict the values of x to be positive.

for f(x) = 4x², x≥0, the inverse function is f⁻¹(x) = (1/2)√x