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
`(f(x)-f(a))/(x-a)`

Here f(x) =
`(1)/(x)`

So f(a) =
`(1)/(a)`

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

We get

f(x) - f(a)

=
`=(1)/(x)-(1)/(a)`

Making denominators same we get

`(a)/(ax)-(x)/(ax)`

So we get

f(x) - f(a) =
`(a-x)/(ax)`

So the difference quotient shall be

`(f(x)-f(a))/((x-a))=((a-x)/(ax))/((x-a)) =(a-x)/(ax(x-a))`

Hence the difference quotient is

`(f(x)-f(a))/((x-a))=(a-x)/(ax(x-a))`