Evaluate the difference quotient for the given function. Simplify your answer.
1/x using the formula f(x)-f(a)/x-a

Question

Evaluate the difference quotient for the given function. Simplify your answer.
 1/x using the formula f(x)-f(a)/x-a

mathmale · Answer

Dear Jasmine, welcome to OpenStudy.

Please, would you provide the instructions for the problem you've posted?  I can easily guess what the goal is, but would prefer that YOU state it for the benefit of yourself and those helping you.

anonymous · Answer

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

anonymous · Answer

please help

mathmale · Answer

You want the difference quotient of f(x) = 1/x.  OK.   Clear.

The difference quotient is defined by $$\frac{ f(x)-f(a) }{ x-a }$$ where x is a variable (corresponding to points along the x axis) and a is a particular, constant x-value.

f(x) = 1/x.  What is f(a) = to?

anonymous · Answer

it doesn't give me fa

mathmale · Answer

You mean, "the problem statement doesn't give me f(a)."  Read that as "function f(x) evaluated at x=a."  

f(x0 = 1/x here.  Simply replace x with a on both sides of the equation.  Result?

anonymous · Answer

1/a

mathmale · Answer

Right.  Now write out (on paper)     f(x) - f(a).  Draw a line under that and underneath, write x-a.   can you do that?

anonymous · Answer

yes

mathmale · Answer

Now re-write the whole thing, replacing f(x) with 1/x   and f(a) with 1/a.

anonymous · Answer

okay

mathmale · Answer

You now have $$\frac{ 1/x - 1/a }{ x-a }$$ and must find and use the LCD of the numerator 1/x - 1/a to combine those two fractions through subtraction.  Familiar with this step?

mathmale · Answer

Hint:  1/3 - 1/4 = (4-3)/12 = 1/12.  Be certain you understand this procedure.

anonymous · Answer

no

mathmale · Answer

In 1/3 - 1/4 the two (different ) denominators are 3 and 4.  Since those 2 have nothing in common, the LCD is 3*4=12, right?

anonymous · Answer

right

mathmale · Answer

So you need to do essentially the same thing with 1/x - 1/a.
The 2 different denoms. are x and a; since they have nothing in common, the LCD here is xa.
OK?

mathmale · Answer

Jasmine, I've checked and have found that you've apparently logged off OpenStudy.  When you have someone helping you with a math problem and decide to log off, PLEASE be courteous and inform your helper.