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How do you express the following function, f(x) as a composition of two functions f and g given #f(x)=x^2/(x^2+4)#?

Answer 1

To express the function ( f(x) = \frac{x^2}{x^2 + 4} ) as a composition of two functions ( f ) and ( g ), you can rewrite it as ( f(g(x)) ).

Let's denote ( g(x) ) as the denominator ( x^2 + 4 ). Then, ( f(g(x)) ) will be ( f(x) = \frac{x^2}{g(x)} ).

So, ( f(x) ) can be expressed as the composition of two functions: ( f(x) = f(g(x)) ).

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Answer 2

James Allen

Find two functions that could go into each other to form that composite function. Multiple answers possible.

ƒ(x) = h(g(x))

h = #x/(x + 4)#

g = #x^2#

ƒ(x) = h(g(x))

Hopefully this answers your question!

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.