Question

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

Answer 1

There are many ways to do this.

One such way is

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

$g(x) = x^2$

So therefore,

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

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

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

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Another way to do it is this

$f(x) = \frac{1}{x}+2$

$g(x) = \frac{1}{8}x^2$

So,

$f(x) = \frac{1}{x}+2$

$f(g(x)) = \frac{1}{g(x)}+2$

$f(g(x)) = \frac{1}{1/8x^2}+2$

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

getting the same result