https://file.aiquickdraw.com/mathbot/file/17269928677676z381z85.jpg

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.

Diberikan dua fungsi f(x) = 3x + 2 dan g(x) = x^2 - 5. Nilai dari h(3) jika h(x) = (f o g)(x) adalah ...

Learn how to solve a function composition problem where f(x) = 3x + 2 and g(x) = x^2 - 5, and find h(3) using the formula h(x) = f(g(x)). This problem covers algebraic concepts and is suitable for Grades 9-11.

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