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:

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