Question

If f(x) = 3x + 3,9(x) = 3x + 3, and h(x) = x + 3, what is [g°f°h](-5)?​

Answer 1

For this case we have the following functions:

`f (x) = 3x + 3\\g (x) = 3x + 3\\h (x) = x + 3`

We must find
`(g_ {o} f_ {o} h) (x).`

By composition of functions we have to:

`(g_ {o} f_ {o} h) (x) = g (f (h (x)))`

So:

`f (h (x)) = 3 (x + 3) + 3 = 3x + 9 + 3 = 3x + 12`

Thus, we have to:

`g (f (h (x))) = 3 (3x + 12) + 3 = 9x + 36 + 3 = 9x + 39`

Finally we have:

`(g_ {o} f_ {o} h) (- 5) = 9 (-5) + 39 = -45 + 39 = -6`

ANswer:

`(g_ {o} f_ {o} h) (- 5) = - 6`