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Determine the domain of the function defined by the given equation.$g(x)=\frac{x+1}{2 x+5}$

$$x \neq-5 / 2$$

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

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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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this problem, we need to determine the domain of our function. G of X. So to answer this, let's take a step back and review what we mean by domain Domain is all of the inputs into our function. It's the X values that are acceptable to plug into our equation. Whatever it ISS on, I wrote that very badly. Let me try writing that word again. Our X values. There we go now, when we're trying to determine which values are acceptable, it's actually often easier to figure out which numbers are unacceptable. And then our domain is everything except those numbers. There are two important things to check for when we're checking for impossible values for the domain. First, if we have a square root everything under that square root that needs to be a positive values. I can't take the square root of a negative and still have a real number. So if I have square roots, I need to check those. And if I have fractions, because if I have a fraction, that denominator can't be zero. I can't divide by zero now for my function g of X. In this problem, I do not have square roots, but I do have fractions. So let's take a look at that denominator. I cannot have the denominator equal zero. When does that occur? Well, if I solve for X, I get X equals negative five halves. So this value negative five halves cannot exist in my domain because that would give me an impossible fraction. But every other number is okay. There's nothing else. I could have zero in the numerator. I can have any X. I want positive. Negative. It doesn't matter with one exception. So for this problem, my domain is all riel numbers except for X equals negative five halfs. That's the Onley number that I have to exclude from my domain.

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