https://file.aiquickdraw.com/mathbot/file/1727483257608c17dnoq3.jpg

Let's solve the two problems shown in the image:

### 1. For \( f(x) = 9x - 5 \), calculate \( f \circ f(-1) \).

The function composition \( f \circ f(-1) \) means that we first find \( f(-1) \), and then apply the function \( f \) again to the result.

- First, calculate \( f(-1) \):
  \[
  f(-1) = 9(-1) - 5 = -9 - 5 = -14
  \]
- Now, apply \( f \) to the result, \( f(-14) \):
  \[
  f(-14) = 9(-14) - 5 = -126 - 5 = -131
  \]
So, \( f \circ f(-1) = -131 \).

---

### 2. For \( g(x) = 4 - x^2 \), calculate \( g \circ g(4) \).

Similar to the first problem, we first find \( g(4) \), and then apply the function \( g \) again to the result.

- First, calculate \( g(4) \):
  \[
  g(4) = 4 - 4^2 = 4 - 16 = -12
  \]
- Now, apply \( g \) to the result, \( g(-12) \):
  \[
  g(-12) = 4 - (-12)^2 = 4 - 144 = -140
  \]
So, \( g \circ g(4) = -140 \).

---

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:
1. What is the general process for finding the composition of two functions?
2. How would you graph \( f(x) = 9x - 5 \) and \( g(x) = 4 - x^2 \)?
3. Can you perform the composition of \( f \circ f(x) \) in general form, not just for \( x = -1 \)?
4. How do you find the inverse of \( f(x) = 9x - 5 \) or \( g(x) = 4 - x^2 \)?
5. How do transformations affect the graph of \( f(x) = 9x - 5 \)?

**Tip:** Always perform function compositions step by step, especially when dealing with different function types like linear and quadratic!

Given that f(x) = 9x - 5, calculate f ∘ f(-1). Given that g(x) = 4 - x^2, calculate g ∘ g(4).

Learn how to calculate the composition of functions with f(x) = 9x - 5 and g(x) = 4 - x^2. This step-by-step solution covers how to solve f ∘ f(-1) and g ∘ g(4), using key algebraic concepts of linear and quadratic functions. Suitable for students in Grades 9-11.

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