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Compute the difference quotient $\frac{f(x+h)-f(x)}{h}, \quad h \neq 0$ Whenever possible, simplify the expression so that the resulting expression is defined when $h=0$.$f(x)=2 / x$

$$\frac{-2}{x(x+h)}$$

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

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University of Michigan - Ann Arbor

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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Compute the difference quo…

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Find and simplify the diff…

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for this problem. We've been given a function f of X equals two divided by X, and for this problem, we're going to compute the difference quotient, which is f of X plus h minus ffx over H. This difference question is something that will see over again in calculus, but for right now, let's evaluate it. So our numerator, we're going to use our function f twice the first time we're going to evaluate it at X plus h and the second time, just a X So x plus h first. That means on our function everywhere where there is an ex, we're going to put an X plus h so we have to over X plus h minus f of X, which is just too over X, and I'm going to divide everything by H. Now we want to simplify. This is much as possible. So let's look at our numerator. First, we've got two fractions which we can subtract if we do a common denominator. So my common denominator would be X times X plus h. That means I'm gonna have to x and minus two times X plus h and I'm dividing this whole thing by H, which means I could just put that h in the denominator. Okay, let's get rid of parentheses in our numerator. See if I can simplify this at all. I have two X minus two X minus two h over x times X plus h times H well, that two X minus two x that cancels. So I have a negative to h on top. Well, that h on top can cancel with the H on the bottom. So what that leaves me with is negative two and in the numerator and x times X plus h in the denominator.

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