We are given the functions $f(x) = 3x + 6$ and $g(x) = -7$, and asked to calculate the following:

Part (a): $f(g(8))$

• First, note that $g(x) = -7$ for all $x$, so $g(8) = -7$.
• Now, substitute this value into $f(x)$: $f(g(8)) = f(-7) = 3(-7) + 6 = -21 + 6 = -15$ So, $f(g(8)) = -15$, which is correctly calculated in the given solution.

Part (d): $g(f(-1))$

• First, calculate $f(-1)$: $f(-1) = 3(-1) + 6 = -3 + 6 = 3$
• Now, substitute this value into $g(x)$. Since $g(x) = -7$ for all $x$, we have: $g(f(-1)) = g(3) = -7$ So, $g(f(-1)) = -7$.

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Here are 5 related questions:

1. What is $f(g(2))$?
2. What is $g(f(0))$?
3. What is $f(f(-2))$?
4. If $g(x) = 2x - 5$, what would $g(f(4))$ be?
5. Can $g(x)$ ever be anything other than -7 for the given function?

Tip: When dealing with function compositions, always evaluate the inner function first, then use the result in the outer function.