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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 $h=0$.$f(x)=3 x-2$

$$3$$

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

Harvey Mudd College

Baylor University

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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Determine the difference q…

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Find and simplify the diff…

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Find the difference quotie…

for this problem. We have been given a function f of X equals three X minus two, and we've been asked to compute the difference quotient. This is a very important question that we use a lot in calculus and it's f of X plus h minus f of X, divided by H. And because we're dividing by H, we always need to so say that H is not equal zero. I'm not dividing by zero here. So how do we evaluate this? Given our function? Well, when you have f of something like this f of X plus h, we're gonna goto our F function. We're gonna plug in X Plus H anywhere that there's an X in their original function. So let's see what we have when we do that f of X plus h Well, that's three times X plus H minus two. That's our f of X plus age. Now we're subtracting f of X, and that's just gonna be minus three X minus two over h. So let's get rid of of some of our parentheses and see if we can simplify. This gives us three X plus three H minus two. We have distribute that negative. So it's minus three X plus two over H. Unfortunately, we have some things to cancel. I have a plus to an A minus two. I have a plus three x and, uh minus three X. So what we're left with is three h on the top over H. And even here are h is will cancel. So when we evaluate this entire expression, we end up with an answer of three.

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