Given that f(x)=9x+4
 and g(x)=2-x^2
, calculate
(a) 
f(g(0))= 
  
(b) 
g(f(0))= 


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.

Given that f(x)=9x+4 and g(x)=2-x^2, calculate (a) f(g(0))= (b) g(f(0))=

Explore the composition of functions f(g(0)) and g(f(0)) with detailed solutions. Learn how to substitute values step-by-step and understand the concepts of function composition in algebra, suitable for Grades 9-10.

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