Respuesta :
The difference quotient of f(x) is [tex]\frac{-\frac{1}{h}+ 5}{5x+ h -12}[/tex] .
According to the given question.
We have a function
f(x) = -1/(5x -12)
As we know that, the difference quotient is a measure of the average rate of change of the function over and interval.
The difference quotient formula of the function y = f(x) is
[f(x + h) - f(x)]/h
Where,
f(x + h) is obtained by replacing x by x + h in f(x)
f(x) is a actual function.
Therefore, the difference quotient formual for the given function f(x)
= [f(x + h) - f(x)]/h
= [tex]\frac{\frac{-1}{5(x+h)-12} -\frac{-1}{5x-12} }{h}[/tex]
= [tex]\frac{\frac{-1}{5x + 5h -12}+\frac{1}{5x-12} }{h}[/tex]
= [tex]\frac{\frac{-1+5h}{5x + 5h-12} }{h}[/tex]
= [tex]\frac{-1+5h}{(5x +h-12)(h)}[/tex]
= [tex]\frac{-1+5h}{5xh + h^{2} -12h}[/tex]
= [tex]\frac{h(-\frac{1}{h}+5) }{h(5x+h-12)}[/tex]
= [tex]\frac{-\frac{1}{h}+ 5}{5x+ h -12}[/tex]
Hence, the difference quotient of f(x) is [tex]\frac{-\frac{1}{h}+ 5}{5x+ h -12}[/tex] .
Find out more information about difference quotient here:
https://brainly.com/question/18270597
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