Question

Find f(x) and g(x) so that the function can be described as y = f(g(x)). y = nine divided by square root of quantity five x plus five.

Answer 1

`y=(9)/(√(5x+5))`
hmm, seems that we can say that the square root thing is the g(x)

I would say

`f(x)=(9)/(x)` and

`g(x)=√(5x+5)`

we could also have

`f(x)=(9)/(√(x))` and

`g(x)=5x+5`

or

`f(x)=(9)/(√(x+5))` and

`g(x)=5x`

there are many posibilities

Answer 2

f(x)=
`(9)/(x)`

g(x)=
`√(5x+5)`

Explanation:

y=
`(9)/(√(5x+5) )`

We have to find f(x) and g(x). There are many possible answers, but we are going to suppose that f(x)=
`(9)/(x)`

to obtain y(x) we should have
`√(5x+5)` in the denominator. We can obtain that by saying that g(x)=
`√(5x+5)` so f(g(x))=
`\frac{9}{sqrt{5x+5}}`