Question

let
\\( f(x) = 10 - x^2 \\), \\( x \ge 0 \\)

\\( f^{-1}(x) = \\)

Explanation:

Step1: Set function equal to y

$$y = 10 - x^2$$

Step2: Swap variables x and y

$$x = 10 - y^2$$

Step3: Isolate the y-squared term

$$y^2 = 10 - x$$

Step4: Solve for y

$$y = \sqrt{10 - x}$$

Answer:

\(f^{-1}(x) = \sqrt{10 - x}\)