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The function h(x) = (5x^2 + 2)^(-1/2) may be viewed as a composite function h(x) = f(g(x)). Find...

Question:

The function {eq}h(x) = (5x^2 + 2)^{- \frac{1}{2}} {/eq} may be viewed as a composite function {eq}h(x) = f(g(x)) {/eq}. Find {eq}f(x) {/eq} and {eq}g(x) {/eq}.

Composite Functions:

For the composite function, there is more than one function whose expression is given. Thus the given expression can be written in terms of the function of the function, also known as composite functions.

Answer and Explanation:


In the problem, it is given that the function {eq}h(x) = (5x^2 + 2)^{- \frac{1}{2}} {/eq} may be viewed as a composite function {eq}h(x) = f(g(x)) {/eq}. So we need to find {eq}f(x) {/eq} and {eq}g(x) {/eq}

Hence let {eq}f(x)= x^{- \frac{1}{2}} {/eq}

and then {eq}g(x) =5x^2 + 2 {/eq}

Thus {eq}f(g(x))= (5x^2 + 2)^{- \frac{1}{2}} \\ = h(x) {/eq} hence f(x ) and g(x) are correctly assumed


Learn more about this topic:

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How to Evaluate Composite Functions

from Math 103: Precalculus

Chapter 8 / Lesson 5
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