https://file.aiquickdraw.com/mathbot/file/1727241633519bkekrwna.jpg

Let's solve the two parts of the problem step by step.

Given:
- \( f(x) = 6x - 5 \)
- \( g(x) = 7 - x^2 \)

### (a) \( f(g(0)) \)

1. First, calculate \( g(0) \):
   \[
   g(0) = 7 - (0)^2 = 7
   \]

2. Now, substitute \( g(0) = 7 \) into \( f(x) \):
   \[
   f(g(0)) = f(7) = 6(7) - 5 = 42 - 5 = 37
   \]

So, \( f(g(0)) = 37 \).

### (b) \( g(f(0)) \)

1. First, calculate \( f(0) \):
   \[
   f(0) = 6(0) - 5 = -5
   \]

2. Now, substitute \( f(0) = -5 \) into \( g(x) \):
   \[
   g(f(0)) = g(-5) = 7 - (-5)^2 = 7 - 25 = -18
   \]

So, \( g(f(0)) = -18 \).

### Final Answers:
- (a) \( f(g(0)) = 37 \)
- (b) \( g(f(0)) = -18 \)

Would you like more details on any step?

Here are 5 related questions you might find interesting:
1. What is the general process for calculating the composition of two functions?
2. How would you solve \( g(f(x)) \) if given a different function for \( f(x) \)?
3. What happens if you reverse the order of function composition, such as calculating \( f(g(x)) \) instead of \( g(f(x)) \)?
4. Can you graph the functions \( f(x) = 6x - 5 \) and \( g(x) = 7 - x^2 \) to visualize the results?
5. What are the domain and range for the composite function \( f(g(x)) \)?

Tip: When working with composite functions, always solve from the inside out, starting with the innermost function.

Given that f(x) = 6x - 5 and g(x) = 7 - x^2, calculate (a) f(g(0)) and (b) g(f(0)).

Learn how to solve function compositions with linear and quadratic functions using f(x) = 6x - 5 and g(x) = 7 - x^2. Follow step-by-step solutions to calculate f(g(0)) and g(f(0)). Suitable for Grades 9-10 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation