The image provides the following mathematical functions and tasks:

Given:

• $f(x) = x^2 - 4$
• $g(x) = 3x + 5$
• $h(x) = 2 - 2x$

Find:

1. $(f \circ g)(2)$
2. $(g \circ h)(4)$
3. $(g \circ f)(2)$

Let's solve each:

1. $(f \circ g)(2)$

This represents $f(g(2))$:

• First, calculate $g(2)$:
  $g(2) = 3(2) + 5 = 6 + 5 = 11$
• Then, calculate $f(11)$:
  $f(11) = 11^2 - 4 = 121 - 4 = 117$

Thus, $(f \circ g)(2) = 117$.

2. $(g \circ h)(4)$

This represents $g(h(4))$:

• First, calculate $h(4)$:
  $h(4) = 2 - 2(4) = 2 - 8 = -6$
• Then, calculate $g(-6)$:
  $g(-6) = 3(-6) + 5 = -18 + 5 = -13$

Thus, $(g \circ h)(4) = -13$.

3. $(g \circ f)(2)$

This represents $g(f(2))$:

• First, calculate $f(2)$:
  $f(2) = 2^2 - 4 = 4 - 4 = 0$
• Then, calculate $g(0)$:
  $g(0) = 3(0) + 5 = 0 + 5 = 5$

Thus, $(g \circ f)(2) = 5$.

Final Answers:

1. $(f \circ g)(2) = 117$
2. $(g \circ h)(4) = -13$
3. $(g \circ f)(2) = 5$

Let me know if you'd like further clarification on any of these steps!

Here are 5 related questions to expand your understanding:

1. What is $(f \circ h)(3)$?
2. How would you calculate $(h \circ f)(-1)$?
3. What is the inverse of $f(x) = x^2 - 4$ for positive $x$?
4. How would you find $(g \circ g)(2)$?
5. How does the composition of functions change if you swap the order, as in $(f \circ g)$ versus $(g \circ f)$?

Tip:

When composing functions, always calculate from the inside out, starting with the innermost function and working outward.