Question

evaluate the difference quotient for the given function. Simplify your answer. f(x)=1/x , (f(x) - f(a))/x-a

Answer 1

fx - a f - a x/ x
That's what I came up with

Answer 2

The formula for difference quotient is $\frac{f(x)-f(a)}{x-a}$

Here f(x) = $\frac{1}{x}$

So f(a) = $\frac{1}{a}$

First we shall find f(x) - f(a)

We get

f(x) - f(a)

=$=\frac{1}{x}-\frac{1}{a}$

Making denominators same we get

$\frac{a}{ax}-\frac{x}{ax}$

So we get

f(x) - f(a) = $\frac{a-x}{ax}$

So the difference quotient shall be

$\frac{f(x)-f(a)}{(x-a)}=\frac{\frac{a-x}{ax}}{(x-a)} =\frac{a-x}{ax(x-a)}$

Hence the difference quotient is

$\frac{f(x)-f(a)}{(x-a)}=\frac{a-x}{ax(x-a)}$