Mathematics

Problem

Suppose

f(x) = 9 - \sqrt{x}

and

g(x) = x^2 + 4

. a. a Find

(f \circ g)(x)

and state its domain and range. b. b Find

(g \circ f)(4)

. c. c Find

(f \circ f)(x)

and state its domain and range.

Intuitive explanation

The key to composition is remembering that the output of one function becomes the input of the other. Here, you're asked to find $f(g(x))$ , which means you substitute the entire expression $g(x) = x^2 + 4$ in place of $x$ in the formula for $f$ . The main insight is to be careful with order of operations—apply the square root only to what's inside it, then subtract from 9.

Intuitive explanation

Browse the problem library