Determine g(x+a)−g(x) for the following function.
g(x)=4x2−6x

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Given function,

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Thus the above answer is right.

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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)