Question

Evaluate the difference quotient for the given function. Simplify your answer.

f(x)=1/x, f(x)- f(a)/x-a

Can someone please show me the steps? I know the answer but I don't quite get how to solve it. I tried but kept getting the wrong simplified answer.

Answer 1

f(x) = 1/x

Then ((f(x) - f(a))/(x-a)

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

Multiply everything by ax/ax

we have

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

= -(a-x)/(ax*(a-x))

= -1/(ax) which is the answer

Answer 2

Oh, I get it now. Thank you!! :)