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**Try this!**
Evaluate the following functions. Show your solutions.

1. \( g(x) = 5x - 7; g(x^2 + 1) \)
2. \( h(x) = \sqrt{x^2 + 2x + 4}; h(2) \)
3. \( k(x) = \frac{3x^2 - 1}{2x + 4}; k(-3) \)
4. \( f(x) = 2x^2 + 5x - 9; f(5x - 2) \)
5. \( g(b) = 4^3; p(c^3) \)

Let's work through these step by step:

### 1. \( g(x) = 5x - 7; g(x^2 + 1) \)
We need to find \( g(x^2 + 1) \).
- Substitute \( x^2 + 1 \) into the function \( g(x) = 5x - 7 \).
  \[
  g(x^2 + 1) = 5(x^2 + 1) - 7 = 5x^2 + 5 - 7 = 5x^2 - 2
  \]
So, \( g(x^2 + 1) = 5x^2 - 2 \).

### 2. \( h(x) = \sqrt{x^2 + 2x + 4}; h(2) \)
We need to find \( h(2) \).
- Substitute \( x = 2 \) into the function \( h(x) \).
  \[
  h(2) = \sqrt{2^2 + 2(2) + 4} = \sqrt{4 + 4 + 4} = \sqrt{12} = 2\sqrt{3}
  \]
So, \( h(2) = 2\sqrt{3} \).

### 3. \( k(x) = \frac{3x^2 - 1}{2x + 4}; k(-3) \)
We need to find \( k(-3) \).
- Substitute \( x = -3 \) into the function \( k(x) \).
  \[
  k(-3) = \frac{3(-3)^2 - 1}{2(-3) + 4} = \frac{3(9) - 1}{-6 + 4} = \frac{27 - 1}{-2} = \frac{26}{-2} = -13
  \]
So, \( k(-3) = -13 \).

### 4. \( f(x) = 2x^2 + 5x - 9; f(5x - 2) \)
We need to find \( f(5x - 2) \).
- Substitute \( 5x - 2 \) into the function \( f(x) \).
  \[
  f(5x - 2) = 2(5x - 2)^2 + 5(5x - 2) - 9
  \]
First, expand \( (5x - 2)^2 \):
  \[
  (5x - 2)^2 = 25x^2 - 20x + 4
  \]
Now, substitute back into the expression for \( f(5x - 2) \):
  \[
  f(5x - 2) = 2(25x^2 - 20x + 4) + 5(5x - 2) - 9 = 50x^2 - 40x + 8 + 25x - 10 - 9
  \]
  \[
  f(5x - 2) = 50x^2 - 15x - 11
  \]
So, \( f(5x - 2) = 50x^2 - 15x - 11 \).

### 5. \( g(b) = 4^3; p(c^3) \)
We are given \( g(b) = 4^3 \), so:
\[
g(b) = 64
\]
For \( p(c^3) \), no explicit function \( p(x) \) is given, so we cannot compute this without more information.

Would you like a more detailed explanation for any of these solutions? Let me know if you have any specific questions!

Here are 5 related questions for further practice:
1. Evaluate \( g(x^2 - 4) \) if \( g(x) = 3x + 5 \).
2. Find \( h(3) \) if \( h(x) = \sqrt{x^2 + 6x + 5} \).
3. Calculate \( k(2) \) if \( k(x) = \frac{2x^2 - x}{x + 1} \).
4. Solve \( f(3x + 1) \) if \( f(x) = x^2 + 3x + 7 \).
5. Compute \( p(x^2 - 1) \) for a given function \( p(x) = 5x + 9 \).

**Tip**: Always simplify expressions before substituting to make calculations easier!

Evaluate the following functions:
1. g(x) = 5x - 7; g(x^2 + 1)
2. h(x) = √(x^2 + 2x + 4); h(2)
3. k(x) = (3x^2 - 1) / (2x + 4); k(-3)
4. f(x) = 2x^2 + 5x - 9; f(5x - 2)
5. g(b) = 4^3; p(c^3)

This math problem set involves evaluating functions through substitution and simplifying expressions, including quadratics and square roots. Detailed step-by-step solutions cover function manipulation and algebraic concepts, ideal for students in Grades 9-12.

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