QuestionFind $f(g(h(x)))$ where $f(x)=x^{4}+4$ , $g(x)=x-7$ , and $h(x)=\sqrt{x}$ .

Studdy Solution

STEP 1

Assumptions1. We have three functions $f(x)=x^{4}+4$ , $g(x)=x-7$ and $h(x)=\sqrt{x}$ . . We need to find the composition of these functions in the order $f(g(h(x)))$ .

STEP 2

First, we need to find the value of $h(x)$ , which is $\sqrt{x}$ .

STEP 3

Next, we substitute $h(x)$ into $g(x)$ to get $g(h(x))$ . $g(h(x)) = g(\sqrt{x}) = \sqrt{x} -7$

STEP 4

Now, we substitute $g(h(x))$ into $f(x)$ to get $f(g(h(x)))$ . $f(g(h(x))) = f(\sqrt{x} -7) = (\sqrt{x} -7)^{4} +4$

STEP 5

implify the expression to get the final result.
$f(g(h(x))) = (\sqrt{x} -7)^{4} +4$ So, $f(g(h(x))) = (\sqrt{x} -7)^{4} +4$ .

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QuestionFind $f(g(h(x)))$ where $f(x)=x^{4}+4$ , $g(x)=x-7$ , and $h(x)=\sqrt{x}$ .

Studdy Solution

STEP 1

Assumptions1. We have three functions $f(x)=x^{4}+4$ , $g(x)=x-7$ and $h(x)=\sqrt{x}$ . . We need to find the composition of these functions in the order $f(g(h(x)))$ .

STEP 2

First, we need to find the value of $h(x)$ , which is $\sqrt{x}$ .

STEP 3

Next, we substitute $h(x)$ into $g(x)$ to get $g(h(x))$ . $g(h(x)) = g(\sqrt{x}) = \sqrt{x} -7$

STEP 4

Now, we substitute $g(h(x))$ into $f(x)$ to get $f(g(h(x)))$ . $f(g(h(x))) = f(\sqrt{x} -7) = (\sqrt{x} -7)^{4} +4$

STEP 5

implify the expression to get the final result.
$f(g(h(x))) = (\sqrt{x} -7)^{4} +4$ So, $f(g(h(x))) = (\sqrt{x} -7)^{4} +4$ .

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QuestionFind f(g(h(x)))f(g(h(x)))f(g(h(x))) where f(x)=x4+4f(x)=x^{4}+4f(x)=x4+4, g(x)=x−7g(x)=x-7g(x)=x−7, and h(x)=xh(x)=\sqrt{x}h(x)=x​.

Studdy Solution

STEP 1

Assumptions1. We have three functions f(x)=x4+4f(x)=x^{4}+4f(x)=x4+4, g(x)=x−7g(x)=x-7g(x)=x−7 and h(x)=xh(x)=\sqrt{x}h(x)=x​. . We need to find the composition of these functions in the order f(g(h(x)))f(g(h(x)))f(g(h(x))).

STEP 2

First, we need to find the value of h(x)h(x)h(x), which is x\sqrt{x}x​.

STEP 3

Next, we substitute h(x)h(x)h(x) into g(x)g(x)g(x) to get g(h(x))g(h(x))g(h(x)).g(h(x))=g(x)=x−7g(h(x)) = g(\sqrt{x}) = \sqrt{x} -7g(h(x))=g(x​)=x​−7

STEP 4

Now, we substitute g(h(x))g(h(x))g(h(x)) into f(x)f(x)f(x) to get f(g(h(x)))f(g(h(x)))f(g(h(x))).f(g(h(x)))=f(x−7)=(x−7)4+4f(g(h(x))) = f(\sqrt{x} -7) = (\sqrt{x} -7)^{4} +4f(g(h(x)))=f(x​−7)=(x​−7)4+4

STEP 5

implify the expression to get the final result.f(g(h(x)))=(x−7)4+4f(g(h(x))) = (\sqrt{x} -7)^{4} +4f(g(h(x)))=(x​−7)4+4So, f(g(h(x)))=(x−7)4+4f(g(h(x))) = (\sqrt{x} -7)^{4} +4f(g(h(x)))=(x​−7)4+4.

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QuestionFind $f(g(h(x)))$ where $f(x)=x^{4}+4$ , $g(x)=x-7$ , and $h(x)=\sqrt{x}$ .

Assumptions1. We have three functions $f(x)=x^{4}+4$ , $g(x)=x-7$ and $h(x)=\sqrt{x}$ . . We need to find the composition of these functions in the order $f(g(h(x)))$ .

First, we need to find the value of $h(x)$ , which is $\sqrt{x}$ .

Next, we substitute $h(x)$ into $g(x)$ to get $g(h(x))$ . $g(h(x)) = g(\sqrt{x}) = \sqrt{x} -7$

Now, we substitute $g(h(x))$ into $f(x)$ to get $f(g(h(x)))$ . $f(g(h(x))) = f(\sqrt{x} -7) = (\sqrt{x} -7)^{4} +4$

implify the expression to get the final result.
$f(g(h(x))) = (\sqrt{x} -7)^{4} +4$ So, $f(g(h(x))) = (\sqrt{x} -7)^{4} +4$ .