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

g(x) − f(x) = 3x − 8 − 5x
g(x) − f(x) = 3x − 10 − 5x
g(x) − f(x) = −2x − 8 − 3x
g(x) − f(x) = −2x − 10 − 3x

Respuesta :

SaniShahbaz

Answer:

[tex]g(x) - f(x) = 3x - 8 - 5x[/tex] is the answer.

Step-by-step explanation:

Considering the parent functions

  • [tex]f(x) = 5x -1[/tex]
  • [tex]g(x) = 3x - 9[/tex]

To Determine:

We have to determine

[tex]g(x) - f(x)[/tex]

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

The difference of [tex]g-f[/tex]

[tex](g-f)(x)=g(x)-f(x)[/tex]

As

  • [tex]f(x) = 5x -1[/tex]
  • [tex]g(x) = 3x - 9[/tex]

So,

[tex](g-f)(x)=g(x)-f(x)[/tex]

And

[tex]g(x) - f(x) = 3x - 9 - (5x - 1)[/tex]

Solving

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

As

[tex]-\left(5x-1\right)[/tex]

[tex]Distribute\:parentheses[/tex]

[tex]=-\left(5x\right)-\left(-1\right)[/tex]

[tex]\mathrm{Apply\:minus-plus\:rules}[/tex]

[tex]-\left(-a\right)=a,\:\:\:-\left(a\right)=-a[/tex]

[tex]=-5x+1[/tex]

So, equation [A] becomes

[tex]3x-9-\left(5x-1\right) = 3x-9-5x+1[/tex]         ∵ [tex]-\left(5x-1\right):\quad -5x+1[/tex]

[tex]3x-9-\left(5x-1\right) = 3x-8-5x[/tex]

Therefore,

[tex]g(x) - f(x) = 3x - 8 - 5x[/tex] is the answer.

Keywords: combining functions, The difference of [tex]g-f[/tex]

Learn more about composition of function from brainly.com/question/12293021

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