Question

Find f(x) and g(x) so the function can be expressed as y = f(g(x)). (1 point)

y = Eight divided by x squared. + 4

Answer 1

`f(x)=x+4`

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

Explanation:

we are given

we are given

`y=(8)/(x^2)+4`

Since, we have to identify f(x) and g(x)

where g(x) is inner function

Let's assume

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

so, we get

`y=g(x)+4`

we know that

y=f(g(x))

so, we can also write as

`f(g(x))=g(x)+4`

now, we can replace g(x) as x

we get

`f(x)=x+4`

so, we get

`f(x)=x+4`

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

Answer 2

`g(x)=x^2+4` and
`f(x)=(8)/(x)`

Explanation:

If we want to express
`y` as
`y=f(g(x))`, this means that put the function
`g(x)` into
`x` of
`f(x)` to get
`y`.

The function
`y` is given as
`y=(8)/(x^(2)+4)`

So we need to figure out a function
`g(x)` that we can put into another
`f(x)` to get
`y`

If we let
`g(x)=x^2+4` and
`f(x)=(8)/(x)`, we can clearly see that putting g(x) into x of f(x) will give us
`(8)/(x^2+4)`, which is y.

Hence
`g(x)=x^2+4` and
`f(x)=(8)/(x)`