Question

If h(x)=(f o g )(x) and h(x)=5(x+1)^3, find one possibility for f(x) and g(x)

Answer 1

The possibilities of f(x) and g(x) are

• 
  `g(x) =x+1` and
  `f(x) = 5x^(3)`

• 
  `g(x) = (x+1)^(3)` and
  `f(x) = 5x`

Explanation:

The given function is
`h(x)=(f o g )(x)` where
`h(x) = 5(x+1)^(3)`

We need to find one possibility for f(x) and g(x),

One of possible solution is;

Let
`g(x) =x+1`

and

`f(x) = 5x^(3)`

Another possible solution is;

Let
`g(x) = (x+1)^(3)`

and

`f(x) = 5x`

Therefore, the possibilities of f(x) and g(x) are

• 
  `g(x) =x+1` and
  `f(x) = 5x^(3)`

• 
  `g(x) = (x+1)^(3)` and
  `f(x) = 5x`

Answer 2

h(x)=(f o g )(x) = f[g(x)] = 5(x+1)³
So, one of possible solution is to let
g(x) = x+1
and
f(x) = 5x³

Another possible solution is to let
g(x) = (x+1)³
and
f(x) = 5x