https://file.aiquickdraw.com/mathbot/file/1727318849297pg0awt34.jpg

Let’s start solving some of the questions from the image.

### 5. The given functions are \( f(x) = 3x^2 + 2x - 1 \) and \( g(x) = x - 1 \). If we form \( h(x) = \frac{f(x)}{g(x)} \), then what is \( h(2) \)?

To solve this:
- We calculate \( f(2) \) and \( g(2) \) first.
  
For \( f(2) \):
\[
f(2) = 3(2)^2 + 2(2) - 1 = 3(4) + 4 - 1 = 12 + 4 - 1 = 15
\]

For \( g(2) \):
\[
g(2) = 2 - 1 = 1
\]

So, \( h(2) = \frac{f(2)}{g(2)} = \frac{15}{1} = 15 \).

Answer: **b. 15**

---

### 6. The function is \( f(x) = 2x^2 - 5x + 3 \). Find \( f(3) \).

We substitute \( x = 3 \) into the function:

\[
f(3) = 2(3)^2 - 5(3) + 3 = 2(9) - 15 + 3 = 18 - 15 + 3 = 6
\]

Answer: **c. 6**

---

### 7. The given functions are \( f(x) = 3x - 1 \) and \( g(x) = 2x^2 + 3 \). Find the value of the composite function \( (g \circ f)(x) \).

First, find \( f(x) \):
\[
f(x) = 3x - 1
\]

Now substitute \( f(x) \) into \( g(x) \):
\[
g(f(x)) = g(3x - 1) = 2(3x - 1)^2 + 3
\]

Expand \( (3x - 1)^2 \):
\[
(3x - 1)^2 = 9x^2 - 6x + 1
\]
Now substitute this back into \( g(f(x)) \):
\[
g(f(x)) = 2(9x^2 - 6x + 1) + 3 = 18x^2 - 12x + 2 + 3 = 18x^2 - 12x + 5
\]

Answer: **b. 18x^2 - 12x + 5**

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### 8. The functions are \( f(x) = 2x^2 + 3 \) and \( g(x) = \sqrt{x + 4} \). Find \( (g \circ f)(2) \).

First, find \( f(2) \):
\[
f(2) = 2(2)^2 + 3 = 2(4) + 3 = 8 + 3 = 11
\]

Now, find \( g(f(2)) = g(11) \):
\[
g(11) = \sqrt{11 + 4} = \sqrt{15}
\]

Answer: **e. \(\sqrt{15}\)**

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### 9. The functions are \( f(x - 1) = 5x^2 + 6x - 6 \) and \( g(x) = ax + 1 \). If \( (g \circ f)(1) = -51 \), find \( f(a + 1) \).

We are asked to find \( f(a + 1) \). First, substitute \( x = 1 \) into \( f(x - 1) \):

\[
f(1 - 1) = 5(1)^2 + 6(1) - 6 = 5 + 6 - 6 = 5
\]

Then, since \( g(1) = -51 \), we must solve for \( f(a + 1) \).

This part is complex, let me confirm details to continue.

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Let me know if you'd like further details on these, or if I can assist with any other specific questions!

Jawab yang tepat untuk soal komposisi fungsi f(x) dan g(x)

Learn how to solve algebraic problems related to function compositions such as f(g(x)) and g(f(x)) for Grades 10-11. Explore step-by-step solutions using quadratic and linear functions.

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