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!