Given functions:

$f(x) = 9x + 4$ $g(x) = 2 - x^2$

Let's calculate each part step by step.

Part (a): $f(g(0))$

1. Find $g(0)$: $g(0) = 2 - (0)^2 = 2$

2. Substitute $g(0) = 2$ into $f(x)$: $f(g(0)) = f(2) = 9 \cdot 2 + 4 = 18 + 4 = 22$

So, $f(g(0)) = 22$

Part (b): $g(f(0))$

1. Find $f(0)$: $f(0) = 9 \cdot 0 + 4 = 4$

2. Substitute $f(0) = 4$ into $g(x)$: $g(f(0)) = g(4) = 2 - (4)^2 = 2 - 16 = -14$

Thus, $g(f(0)) = -14$

Final Answers:

• $f(g(0)) = 22$
• $g(f(0)) = -14$

Would you like further explanation on function composition or any specific steps?

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Related Questions:

1. What is $f(g(x))$ in general form?
2. What is $g(f(x))$ in general form?
3. How would $f(g(x))$ and $g(f(x))$ change if the functions were shifted?
4. If $h(x) = f(g(x))$, how would you find the derivative $h'(x)$?
5. How do these operations affect the domain and range of the resulting functions?

Tip:

When composing functions, always start with the innermost function and work outward step-by-step.