inverse of y=sqrt(x+1) — step-by-step solution

The function is strictly monotone on

x \geq -1

: it has an inverse on its range

y \geq 0

Isolate the square root:

\sqrt{x + 1} = y

, with

y \geq 0

. Under this condition, squaring gives

x + 1 = y^{2}

⇥Let's solve in

ℝ

x + 1 = y^{2}

⇥Solution obtained:

x = y^{2} - 1

Renaming the output as

x

, the inverse is

x^{2} - 1

, with domain

x \geq 0

▶Inverse function:

(x^{2} - 1 for x \geq 0)