The difference quotient for the function [tex]f(x) = -\frac{1}{5x-12}[/tex] is [tex]\frac{5}{(5x+5h-12)(5x-12)};[/tex] h≠0
Option B) is the correct answer.
What is the difference quotient for [tex]f(x) = -\frac{1}{5x-12}[/tex] ?
Given that;
- [tex]f(x) = -\frac{1}{5x-12}[/tex]
- difference quotient for f(x) = ?
We know that difference quotient is expressed as;
[tex]\frac{f(x+h)-f(x)}{h}[/tex]
Next, substitute x+h for x.
Hence;
[tex]f(x+h) = -\frac{1}{5(x+h)-12}[/tex]
Now,
[tex]\frac{f(x+h)-f(x)}{h} = \frac{-\frac{1}{5(x+h)-12}-(-\frac{1}{5x-12}) }{h} \\\\= \frac{5}{(5x-12)(5h+5x-12)}\\\\= \frac{5}{(5x+5h-12)(5x-12)};[/tex]h≠0
The difference quotient for the function [tex]f(x) = -\frac{1}{5x-12}[/tex] is [tex]\frac{5}{(5x+5h-12)(5x-12)};[/tex] h≠0
Option B) is the correct answer.
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