Question

homework assignment 1.4: composition of functions
score: 5/11 answered: 5/11
question 7
if $f(x) = x^4 + 6$, $g(x) = x - 7$ and $h(x) = \sqrt{x}$, then
$f(g(h(x))) = \square$.
question help: video written example

Explanation:

Step1: Find g(h(x))

First, substitute \( h(x) \) into \( g(x) \). Since \( h(x)=\sqrt{x} \) and \( g(x)=x - 7 \), we replace \( x \) in \( g(x) \) with \( \sqrt{x} \). So \( g(h(x))=g(\sqrt{x})=\sqrt{x}-7 \).

Step2: Find f(g(h(x)))

Next, substitute \( g(h(x)) \) into \( f(x) \). Since \( f(x)=x^{4}+6 \) and \( g(h(x))=\sqrt{x}-7 \), we replace \( x \) in \( f(x) \) with \( \sqrt{x}-7 \). So \( f(g(h(x)))=(\sqrt{x}-7)^{4}+6 \).

Answer:

\((\sqrt{x} - 7)^4 + 6\)