QuestionFind $(g \circ f \circ h)(x)$ for $f(x)=4x-8$ , $g(x)=x^4$ , and $h(x)=\sqrt[5]{x}$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)=4x-8$ . The function $g(x)=x^{4}$
3. The function $h(x)=\sqrt[5]{x}$
4. The operation $(g \circ f \circ h)(x)$ represents function composition, which means that the output of one function becomes the input of the next function.

STEP 2

We start by finding $f(h(x))$ . We substitute $h(x)$ into the function $f(x)$ .
$f(h(x)) =4h(x) -8$

STEP 3

Now, substitute the actual function of $h(x)$ into the equation.
$f(h(x)) =\sqrt[5]{x} -8$

STEP 4

Now, we need to find $(g \circ f \circ h)(x)$ , which means we substitute $f(h(x))$ into the function $g(x)$ .
$g(f(h(x))) = (4\sqrt[]{x} -8)^{4}$

STEP 5

This is the final step, where we have found the function $(g \circ f \circ h)(x)$ .
So, $(g \circ f \circ h)(x) = (4\sqrt[5]{x} -8)^{4}$

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