University:
Kentucky State University
Course:
MAT 120 | Precalculus
Academic year:

2021
Views:

115

Pages:

6
Author:

Arielle Armstrong

**Composition of Function** 28/Oct/2021 **1. Definition:** Given two functions f and g, the composite (fog) defined by fog(x) = f(g(x)); f o g = f circle g **Example:** g f 2 -> 8 -> 12 9 -> 7 -> 14 10 -> 2 -> 20 fog(2) = f(g(2)) = f(8) = 12 fog(9) = f(g(9)) = f(7) = 14 fog(10) = f(g(10)) = f(2) = 20 fog(4) is undefined **Example:** f(x) = 10-x², g(x) = √(x+1); find fog(x), gof(x)? **1. fog(x) = f(g(x))** = 10 - (√(x+1))² = 10 - (x+1) = 10 - x - 1 = 9 - x **2. gof(x) = g(f(x))** = √(10-x²) + 1 **Example:** f(x) = x² + 1, g(x) = √3x; find fog(1), gof(0) **1. fog(1) = f(g(1))** = √3 * 1 = √3 = √3² + 1 = 3 + 1 = 4 **2. gof(0) = g(f(0))** = √3 * 0 = 0 g(0) = √3 **Examples:** Let fog(x) = 6x^2 - 10x + 5 & f(x) = 2x + 1, find g(0)? fog(x) = 6x^2 - 10x + 5 f(g(x)) = 6x^2 - 10x + 5 2g(x) + 1 = 6x^2 - 10x + 5 2g(0) + 1 = 6(0)^2 - 10(0) + 5 2g(0) + 1 = 5 2g(0) = 4 g(0) = 2 Example: If f(3x+5) = 6x + 11, then f(x) = ? 3x + 5 = y x = (y-5)/3 f(y) = 2(y-5)/3 + 11 f(x) = 2x + 1