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PLEASE HELP 50 PTS


Which expression represents the difference quotient of the function f (x) = negative StartRoot 8 x minus 35 EndRoot?


StartFraction 1 Over negative StartRoot 8 x + h minus 35 EndRoot + StartRoot 3 x minus 35 EndRoot EndFraction; h ≠ 0

StartFraction 1 Over negative StartRoot 8 x + h minus 35 EndRoot minus StartRoot 3 x minus 35 EndRoot EndFraction; h ≠ 0

StartFraction 8 Over negative StartRoot 8 x + h minus 35 EndRoot + StartRoot 3 x minus 35 EndRoot EndFraction; h ≠ 0

StartFraction 8 Over negative StartRoot 8 x + h minus 35 EndRoot minus StartRoot 3 x minus 35 EndRoot EndFraction; h ≠ 0

PLEASE HELP 50 PTS Which expression represents the difference quotient of the function f x negative StartRoot 8 x minus 35 EndRoot StartFraction 1 Over

Answer :

The option fourth represents the difference quotient of the function f(x) option fourth is correct.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

[tex]\rm f(x) = - \sqrt{8x-35}[/tex]

[tex]\rm f(x+h) = - \sqrt{8(x+h)-35}\\\\\rm f(x+h) = - \sqrt{8x+8h-35}\\\\[/tex]

Difference quotient:

[tex]\rm = \dfrac{f(x+h)-f(x)}{h}[/tex]

[tex]\rm = \dfrac{- \sqrt{8x+8h-35}+ \sqrt{8x-35}}{h}[/tex]

After rationalization;

[tex]\rm = \dfrac{- \sqrt{8x+8h-35}+ \sqrt{8x-35}}{h} \times \dfrac{ \sqrt{8x+8h-35}+ \sqrt{8x-35}}{\sqrt{8x+8h-35}+ \sqrt{8x-35}}[/tex]

[tex]\rm = \dfrac{8}{-\sqrt{8x+8h-35}- \sqrt{8x-35} }[/tex] , h ≠ 0

Thus, the option fourth represents the difference quotient of the function f(x) option fourth is correct.

Learn more about the function here:

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