Answer
$H$
Work Step by Step
For these types of problems where we are given a value to plug into composite functions, we evaluate the inner function first using the given value. Then we use the output of the inner function and substitute it where we see $x$ in the outer function. We can write this composite function as $h(g(1))$:
Let's plug in the number $1$ for $x$ in the inner function $g(x)$:
$g(1) = 1 - 3$
Subtract to solve:
$g(1) = -2$
Now, we will use the output $-2$ to plug in for $x$ in the outer function $h(x)$:
$h(g(1)) = (-2)^2 + 6$
Evaluate exponents first, according to order of operations:
$h(g(1)) = 4 + 6$
Add to simplify:
$h(g(1)) = 10$
This value corresponds to option $H$.
