Based on my analysis of the image, I can now provide a complete solution to the problems presented.
The worksheet is titled "Composition of Functions" and asks students to find various combinations of functions f(x) and g(x), where:
- f(x) = 4x - 5
- g(x) = x² + 2x - 3
The problems involve basic function operations (addition, subtraction, multiplication, division) as well as composition of functions (f(g(x)) and g(f(x))).
Here's a breakdown of the solutions:
Function Operations:
1. (f+g)(x) = f(x) + g(x) = (4x - 5) + (x² + 2x - 3) = x² + 6x - 8
2. (f-g)(x) = f(x) - g(x) = (4x - 5) - (x² + 2x - 3) = -x² + 2x - 2
3. (f•g)(x) = f(x) × g(x) = (4x - 5)(x² + 2x - 3) = 4x³ + 8x² - 12x - 5x² - 10x + 15 = 4x³ + 3x² - 22x + 15
4. (f/g)(x) = f(x) ÷ g(x) = (4x - 5)/(x² + 2x - 3)
Function Composition Evaluations:
1. f(g(10)) = f(10² + 2×10 - 3) = f(100 + 20 - 3) = f(117) = 4×117 - 5 = 468 - 5 = 463
2. g(f(-2)) = g(4×(-2) - 5) = g(-8 - 5) = g(-13) = (-13)² + 2×(-13) - 3 = 169 - 26 - 3 = 140
3. f(g(0)) = f(0² + 2×0 - 3) = f(-3) = 4×(-3) - 5 = -12 - 5 = -17
4. g(f(3)) = g(4×3 - 5) = g(12 - 5) = g(7) = 7² + 2×7 - 3 = 49 + 14 - 3 = 60
The handwritten solutions in the image appear to be correct for the problems shown. The worksheet is designed to help students practice both basic function operations and more complex function compositions.
This completes the solution to the problems presented in the image.
Parent Tip: Review the logic above to help your child master the concept of composition functions worksheet.
