The image contains the following mathematical problems that need solutions:

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

Solutions:

1. $g(x) = 5x - 7$, find $g(x + 1)$.

To solve $g(x + 1)$, substitute $x + 1$ into the function $g(x)$: $g(x + 1) = 5(x + 1) - 7 = 5x + 5 - 7 = 5x - 2$ So, $g(x + 1) = 5x - 2$.

2. $h(x) = \sqrt{x^2 + 2x + 4}$, find $h(2)$.

To solve $h(2)$, 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. $k(x) = \frac{3x - 2}{2x + 4}$, find $k(-3)$.

To solve $k(-3)$, substitute $x = -3$ into the function $k(x)$: $k(-3) = \frac{3(-3) - 2}{2(-3) + 4} = \frac{-9 - 2}{-6 + 4} = \frac{-11}{-2} = \frac{11}{2}$ So, $k(-3) = \frac{11}{2}$.

4. $f(x) = 2x^2 + 5x - 9$, find $f(5x - 2)$.

We need to substitute $5x - 2$ for $x$ in 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: $f(5x - 2) = 2(25x^2 - 20x + 4) + 5(5x - 2) - 9 = 50x^2 - 40x + 8 + 25x - 10 - 9$ Simplify: $f(5x - 2) = 50x^2 - 15x - 11$

5. $g(p) = 4p$, find $p\left(\frac{3}{2}\right)$.

Since $g(p) = 4p$, we can evaluate $g\left(\frac{3}{2}\right)$: $g\left(\frac{3}{2}\right) = 4 \times \frac{3}{2} = 6$ So, $g\left(\frac{3}{2}\right) = 6$.

Summary of Results:

1. $g(x + 1) = 5x - 2$
2. $h(2) = 2\sqrt{3}$
3. $k(-3) = \frac{11}{2}$
4. $f(5x - 2) = 50x^2 - 15x - 11$
5. $g\left(\frac{3}{2}\right) = 6$

Would you like further details on any step? Here are five related questions for practice:

1. How would you solve $g(x + 2)$ if $g(x) = 5x - 7$?
2. What is the domain of $h(x) = \sqrt{x^2 + 2x + 4}$?
3. Can you simplify the expression for $k(x) = \frac{3x - 2}{2x + 4}$ in general?
4. How would $f(x) = 2x^2 + 5x - 9$ change if $f(3x - 4)$ was required?
5. What are the intercepts of $g(p) = 4p$?

Tip: Always start by simplifying your algebraic expressions before substituting the values.