Question

Given the parent functions f(x) = 5x –1 and g(x) = 3x –9, what is g(x) –f(x)?

Answer 1

Answer: $g(x)-f(x)=-2x-8$

Step-by-step explanation:

Given parent functions : $f(x)=5x-1\text{ and }g(x)=3x-9$

Then ,

$g(x)-f(x)=3x-9-(5x-1)\\\\\Rightarrow g(x)-f(x)=3x-9-5x+1\ \ \text{[Open brackets]}\\\\\Rightarrow g(x)-f(x)=3x-5x-9+1\ \ \text{[Combine like terms]}\\\\\Rightarrow g(x)-f(x)=-2x-8$

Hence, for the given parent function f(x) and g(x), $g(x)-f(x)=-2x-8$

Answer 2

 g(x) –f(x) = 3x –9 - (5x –1)
 g(x) –f(x) = 3x –9 - 5x + 1
 g(x) –f(x) = -2x - 8

hope it helps