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Determine the domain of the function defined by the given equation.$f(x)=\frac{3 x+2}{2 x-3}$

$$x \neq 3 / 2$$

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

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Harvey Mudd College

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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Determine the domain of th…

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Find the domain of the fun…

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01:31

for this problem, we need to determine the domain of our function f of X. So let's take a step back and review what a domain is. Well, the domain of a function are your input values. They are the X numbers that you are allowed to put into the function. And typically, when we're trying to find domain, the easiest way to figure out what values we can put in is to figure out which numbers we can't put in. And we have. Then the domain is everything except the things that are impossible. Now there's two basic places that we always need to look when we're looking at domain. If we have square roots because you have to have positive numbers under a square root and when we have fractions, because when we have a fraction, the denominator can't be zero. We don't have any square roots here, but we do have a fraction. So we need to make sure that our denominator two x minus three it can't equal zero. So for what value does it equals zero? Well, if I solve this for X, I end up with ex equaling three halves. So for this problem, X cannot equal three halves that is excluded from my domain because it would mean I would divide by zero. Every other number is acceptable. So my domain is all really numbers except X equals three halfs. That would be the domain for my function F of X.

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