Question

Express the given function h as a composition of two functions f and g so that h left parenthesis x right parenthesis equals left parenthesis f circle g right parenthesis left parenthesis x right parenthesis comma where one of the functions is x Superscript 9 Baseline minus 5.
h left parenthesis x right parenthesis equals RootIndex 4 StartRoot x Superscript 9 Baseline minus 5 EndRoot
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Part 1
f left parenthesis x right parenthesisequals
  
enter your response here ​(Simplify your​ answer.)

Answer 1

To express the function \( h(x) = \sqrt[4]{x^9 - 5} \) as a composition of two functions \( f \) and \( g \), we need to identify appropriate functions.

Given that one of the functions is \( x^9 - 5 \), we can let:

1. Define \( g(x) = x^9 - 5 \).
2. Define \( f(x) = \sqrt[4]{x} \).

Now, we can combine these into the composition \( h(x) = (f \circ g)(x) \).

Putting it together, we have:

- \( g(x) = x^9 - 5 \)
- \( f(x) = \sqrt[4]{x} \)

Thus,

\[
h(x) = f(g(x)) = f(x^9 - 5) = \sqrt[4]{x^9 - 5}
\]

Part 1:
Now, we express \( f(x) \):

\[
f(x) = \sqrt[4]{x}
\]

So the final answers would be:
- \( f(x) = \sqrt[4]{x} \)
- \( g(x) = x^9 - 5 \)