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

## Question:

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.

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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...