Question

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

y = eight divided by x squared + 2

Answer 1

There are many ways to do this.

One such way is

`f(x) = (8)/(x)+2`

`g(x) = x^2`

So therefore,

`f(x) = (8)/(x)+2`

`f(g(x)) = (8)/(g(x))+2`

`f(g(x)) = (8)/(x^2)+2`

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Another way to do it is this

`f(x) = (1)/(x)+2`

`g(x) = (1)/(8)x^2`

So,

`f(x) = (1)/(x)+2`

`f(g(x)) = (1)/(g(x))+2`

`f(g(x)) = (1)/(1/8x^2)+2`

`f(g(x)) = (8)/(x^2)+2`

getting the same result