Question

Help me with this, please

Answer 1

One possible set of functions is

`q(x) = √(x) -5` and
`r(x) = 3x^5`

Explanation:

The way to tackle problems of this sort is to remember that the inner function is executed first and its output is fed to the outer function

Inner function is
`r(x)`

Outer function is
`q(x)`

Set
`r(x)` as a function of x. This can be done by a convenient substitution Let's set
`r(x) = 3x^5`

We have

`q(r(x) = √(3x^5) + 5`

Simply replace
`3x^5` with x to get

`q(x) = √(x) - 5`

So two possible functions that satisfy the composition

`q(r(x)) =`
`√(3x^5) + 5`

are

`q(x) = √(x) -5` and

`r(x) = 3x^5`

We can verify this by working out
`q(r(x))` using the above functions. Remember it is the inner function that is executed first

`r(x) =3x^5`

`q(r(x)) = q(3x^5)`

But
`q(x) = √(x) - 5`

Substitute x with
`3x^5` to get
`√(3x^5) - 5`