Question

Given the parent functions f(x) = 5x − 1 and g(x) = 3x − 9, what is g(x) − f(x)? (2 points)

Answer 1

Answer:

$g(x) - f(x) = 3x - 8 - 5x$ is the answer.

Step-by-step explanation:

Considering the parent functions

• $f(x) = 5x -1$

• $g(x) = 3x - 9$

To Determine:

We have to determine

$g(x) - f(x)$

To find the difference between two function, subtract the first from the second.

The difference of $g-f$

$(g-f)(x)=g(x)-f(x)$

As

• $f(x) = 5x -1$

• $g(x) = 3x - 9$

So,

$(g-f)(x)=g(x)-f(x)$

And

$g(x) - f(x) = 3x - 9 - (5x - 1)$

Solving

$3x-9-\left(5x-1\right)....[A]$

As

$-\left(5x-1\right)$

$Distribute\:parentheses$

$=-\left(5x\right)-\left(-1\right)$

$\mathrm{Apply\:minus-plus\:rules}$

$-\left(-a\right)=a,\:\:\:-\left(a\right)=-a$

$=-5x+1$

So, equation [A] becomes

$3x-9-\left(5x-1\right) = 3x-9-5x+1$         ∵ $-\left(5x-1\right):\quad -5x+1$

$3x-9-\left(5x-1\right) = 3x-8-5x$

Therefore,

$g(x) - f(x) = 3x - 8 - 5x$ is the answer.

Keywords: combining functions, The difference of $g-f$

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