Question

What is the inverse of
f(x) = (2x + 1)² for
x ≥ − 1/2?

Answer 1

Answer:
`f^(-1)(x)=(√(x)-1)/(2)`

Explanation:

Let
`f(y)=x`.

`x=(2y+1)^2\\\\\pm √(x)=2y+1\\\\-1 \pm √(x)=2y\\\\y=-(1)/(2) \pm (√(x))/(2)`

Since the domain of the original function is the same as the range of the inverse, the rate of
`f^(-1)(x)` is
`f^(-1)(x) \geq -1/2`. This means we consider the positive case.

`\therefore f^(-1)(x)=(√(x)-1)/(2)`