inverse of f(x)=sqrt(10-x) — step-by-step solution

The function is strictly monotone on

x \leq 10

: it has an inverse on its range

y \geq 0

Isolate the square root:

\sqrt{10 - x} = y

, with

y \geq 0

. Under this condition, squaring gives

10 - x = y^{2}

⇥Let's solve in

ℝ

10 - x = y^{2}

⇥ⓘ We gather the terms in

x

on the right and the other terms on the left

⇥

10 - y^{2} = x

⇥Solution obtained:

x = 10 - y^{2}

Renaming the output as

x

, the inverse is

10 - x^{2}

, with domain

x \geq 0

▶Inverse function:

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