Given the parent functions f(x) = 3x + 2 and g(x) = 5x − 10, what is g(x) − f(x)?

Solution:

Given:

Two functions f(x) and g(x)

f(x) = 3x + 2

g(x) = 5x − 10

From the question

g(x) − f(x) = (5x - 10) - (3x + 2)

By further calculation

g(x) − f(x) = 5x - 10 - 3x - 2

So we get

g(x) − f(x) = 5x - 3x - 10 - 2

g(x) − f(x) = 2x - 12

Therefore, g(x) − f(x) = 2x - 12.

Given the parent functions f(x) = 3x + 2 and g(x) = 5x − 10, what is g(x) − f(x)?

Summary:

Given the parent functions f(x) = 3x + 2 and g(x) = 5x − 10, g(x) − f(x) is (2x - 12).