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Consider the function f and g f(x)= 4x^2 + 1 g(x) x^2-3 perform the function composition

Consider the function f and g f(x)= 4x^2 + 1 g(x) x^2-3 perform the function composition-example-1

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Recall that:


(h\circ l)(x)=h(l(x)).

Therefore, to find the composite functions, first, we evaluate f(x) at:


x^2-3

and get:


f(x^2-3)=4(x^2-3)^2+1.

Simplifying the above result, we get:


f(g(x))=4(x^4-6x^2+9)+1=4x^4-24x^2+37.

Now, we evaluate g(x) at:


4x^2+1

and get:


g(4x^2+1)=(4x^2+1)^2-3.

Simplifying the above result, we get:


g(f(x))=16x^4+8x^2-2.

Answer:


\begin{gathered} f(g(x))=4x^4-24x^2+37, \\ g(f(x))=16x^4+8x^2-2. \end{gathered}

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