Find $\frac { f ( x + h ) - f ( x ) } { h }$ for the given function.
-$$f ( x ) = \frac { 1 } { x - 4 }$$
A) $- \frac { 1 } { ( x - 4 ) ( x + h - 4 ) }$
B) $\frac { 1 } { ( x - 4 ) ( x + h - 4 ) }$
C) $- \frac { 1 } { 2 x + h - 8 }$
D) $\frac { 1 } { 2 x + h - 8 }$

Question

Quizplus · Accepted Answer

To find $\frac{f(x + h) - f(x)}{h}$ for $f(x) = \frac{1}{x - 4}$, we substitute $f(x + h) = \frac{1}{(x + h) - 4}$ and $f(x) = \frac{1}{x - 4}$ into the expression. Simplifying, we get $\frac{\frac{1}{x + h - 4} - \frac{1}{x - 4}}{h}$. Finding a common denominator and simplifying further, we end up with $-\frac{1}{(x - 4)(x + h - 4)}$, which matches choice A.

Find f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​

Find $\frac { f ( x + h ) - f ( x ) } { h }$