Respuesta :

marcthemathtutor

Answer:

8ax + (4a²- 6a)

Step-by-step explanation:

g(x)=4x²−6x

g(x+a)

= 4(x+a)² - 6(x+a)

= 4( x² + 2ax + a²) - 6x - 6a

= 4x² + (4)2ax + (4)a² - 6x - 6a

= 4x² + 8ax + 4a² - 6x - 6a

= 4x² + 8ax  - 6x + 4a²- 6a

= 4x² + (8a  - 6)x + (4a²- 6a)

g(x+a) - g(x)

= [4x² + (8a  - 6)x + (4a²- 6a)] - (4x²−6x)

=  4x² + (8a  - 6)x + (4a²- 6a) - 4x² + 6x

= (8a  - 6)x + (4a²- 6a) + 6x

= (8a  - 6 + 6)x + (4a²- 6a)

= 8ax + (4a²- 6a)

Cricetus

"[tex]-8ax-4a^2-6a[/tex]" is the value of the "[tex]g(x+a)-g(x)[/tex]".

Given function,

  • [tex]g(x)=4x^2-6x[/tex]

Now,

→ [tex]g(x+a) = -4(x+a)^2-6(x+a)[/tex]

                [tex]= -4(x^2+2ax+a^2)-6x-6a[/tex]

                [tex]= -4x^2-8ax-4a^2-6x-5a[/tex]

then,

→ [tex]g(x+a)-g(x) = (-4x^2-8ax-4a^2-6x-6a) -(-4x^2-6x)[/tex]

                           [tex]= -4x^2-8ax-4a^2-6x-6a+4x^2+6x[/tex]

                           [tex]= -8ax-4a^2-6a[/tex]

Thus the above answer is right.

Learn more about function here:

https://brainly.com/question/2254332

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