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:

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