The problem in the image asks us to evaluate the composition of functions and solve for $h(3)$ given two functions $f(x)$ and $g(x)$.

From the image, the two functions provided are: $f(x) = 3x + 2$ and $g(x) = x^2 - 5$

We are tasked with finding $h(3)$, where $h(x) = (f \circ g)(x)$, which means $h(x) = f(g(x))$. This involves composing the two functions and then evaluating the result at $x = 3$.

Step 1: Find $f(g(x))$

Substitute $g(x)$ into $f(x)$: $f(g(x)) = f(x^2 - 5) = 3(x^2 - 5) + 2$ Simplify: $f(g(x)) = 3x^2 - 15 + 2 = 3x^2 - 13$ Thus, $h(x) = 3x^2 - 13$.

Step 2: Evaluate $h(3)$

Now substitute $x = 3$ into $h(x)$: $h(3) = 3(3^2) - 13 = 3(9) - 13 = 27 - 13 = 14$

So, the value of $h(3)$ is $14$.

Would you like more details or have any questions about this solution?

Here are five related questions you might find interesting:

1. How do you generally compose two functions?
2. What happens when we reverse the composition, i.e., $g(f(x))$?
3. Can you explain the domain and range of the composed function $f(g(x))$?
4. How would you solve $h(x) = 0$ for this problem?
5. How does the behavior of quadratic and linear functions affect their composition?

Tip: When composing functions, always work from the inside out, starting with the innermost function.