Question

G(x)=9+4x

h(x)=x+21÷5
Write (h×g)(x) as an
expression in terms of x.
(h×g)(x) =
​

Answer 1

For this case we have the following functions:

`g (x) = 9 + 4x\\h (x) = \frac {x + 21} {5}`

We must find
`(h * g) (x)`. By definition of composite functions we have to:

`(h * g) (x) = h (x) * g (x)`

So:

`(h * g) (x) = 9 + 4x * \frac {x + 21} {5}`

We apply distributive property:

`(h * g) (x) = \frac {9x + 9 * 21 + 4x ^ 2 + 4x * 21} {5}\\(h * g) (x) = \frac {9x + 189 + 4x ^ 2 + 84x} {5}\\(h * g) (x) = \frac {4x ^ 2 + 93x + 189} {5}\\`

Answer:

`(h * g) (x) = \frac {4x ^ 2 + 93x + 189} {5}`