Find {eq}\displaystyle{ \rm f(x) \ and \ g(x) \ if \ h(f) = (f \circ g)(x)=\frac{5 }{ x^2 }+6. } {/eq}


Find {eq}\displaystyle{ \rm f(x) \ and \ g(x) \ if \ h(f) = (f \circ g)(x)=\frac{5 }{ x^2 }+6. } {/eq}

Functions & Compositions

A composition of two functions, {eq}a(x) {/eq} and {eq}b(x) {/eq} is defined as a resultant function {eq}c(x) {/eq}, such that {eq}c(x) = a(b(x)) {/eq}. In order to compose these two functions, we have to:

  • Define the function {eq}b(x) {/eq}.
  • Replace all the independent variables of {eq}a(x) {/eq} with the whole expression of {eq}b(x) {/eq}.
  • The resultant composition is {eq}c(x) = a(b(x)) {/eq} which is a new independent function.

Answer and Explanation: 1

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Given the composition:

{eq}h(x) = f(g(x)) = \dfrac{5}{x^2} + 6 {/eq}

The composition is obtained substituting the function {eq}g(x) {/eq} into...

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Learn more about this topic:

How to Compose Functions


Chapter 7 / Lesson 5

Function composition refers to integrating or the combining of multiple functions, often simplifying them in the process. Discover how the rules of functional notation apply to composing functions through two different example problems.

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