Given that f(x)=5x+6 and g(x)=9−x2g(x)=9-$$ x^2 $$, calculate
(a) f(g(0))= 
(b) g(f(0))=


To solve the problem, we'll first calculate the functions $ f(x) $ and $ g(x) $ using the given expressions and then substitute the values as needed.

Given:
- $ f(x) = 5x + 6 $
- $ g(x) = 9 - x^2 $

### (a) Calculate $ f(g(0)) $:

1. First, find $ g(0) $:
   \[
   g(0) = 9 - (0)^2 = 9 - 0 = 9
   \]

2. Now, substitute $ g(0) = 9 $ into $ f(x) $:
   \[
   f(g(0)) = f(9) = 5(9) + 6 = 45 + 6 = 51
   \]

So, $ f(g(0)) = 51 $.

### (b) Calculate $ g(f(0)) $:

1. First, find $ f(0) $:
   \[
   f(0) = 5(0) + 6 = 0 + 6 = 6
   \]

2. Now, substitute $ f(0) = 6 $ into $ g(x) $:
   \[
   g(f(0)) = g(6) = 9 - (6)^2 = 9 - 36 = -27
   \]

So, $ g(f(0)) = -27 $.

### Final Answers:
- $ f(g(0)) = 51 $
- $ g(f(0)) = -27 $

Do you have any questions or need more details?

### Related Questions:
1. What is the value of $ f(f(2)) $?
2. Calculate $ g(g(1)) $.
3. What is the inverse function of $ f(x) = 5x + 6 $?
4. If $ h(x) = f(x) + g(x) $, what is $ h(1) $?
5. Determine the values of $ x $ where $ f(x) = g(x) $.

### Tip:
When working with composite functions, always evaluate the inner function first before substituting into the outer function.

Learn how to calculate composite functions f(g(0)) and g(f(0)) step-by-step. Understand the application of substitution in algebraic functions. Suitable for high school students and above.

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