Question

Find f(x) and g(x) so the function can be expressed as y = f(g(x)).

y = Eight divided by x squared. + 4

Answer 1

$\bf \begin{cases} f(x)=\cfrac{8}{x}+4\\\\ g(x)=x^2 \end{cases}\qquad f(\ g(x)\ )=\cfrac{8}{\underline{g(x)}}+4\implies f(\ g(x)\ )=\cfrac{8}{\underline{x^2}}+4$

Answer 2

We have that The function can be expressed as $y = f(g(x))$

when

$g(x)=x^2$ and $F(x)=\frac{8}{x}+4$

From calculation below

From the question we are told that:

$Y=\frac{8}{x^2}+4$

Generally for The function y to be expressed as  $f(g(x))$

We have

$Y= f(g(x)).$

And

$Y=\frac{8}{x^2}+4$

Therefore

$f(g(x))=\frac{8}{x^2}+4$

Given that

$g(x)=x^2$

We have

$Y=\frac{8}{g(x)}+4$

Therefore

$F(x)=\frac{8}{x}+4$

In Conclusion

The function can be expressed as $y = f(g(x))$

if

$g(x)=x^2$

and

$F(x)=\frac{8}{x}+4$

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