<h2>Domain and Range of a Function</h2><h3>
Answer:</h3>
Domain:
Range:
<h3>
Step-by-step explanation:</h3>
Domain:
In finding the Domain of a function, the values for the input of the function should not make the output of the function <em>undefined</em> or <em>complex</em>. Because of this, we can think of the values for the input that make the output of the function <em>undefined</em> or <em>complex</em> so that we will <u>not include them in our Domain</u>. We can only make the output <em>undefined</em> if the input makes the denominator . In , there's no value for that makes the denominator as it is constant, (Note: All expressions implicitly have as their denominator even though it's not written). We can only make the output of the function <em>complex</em> if the value of makes the function take the root of a negative number where . There's no radical sign in so we shouldn't worry about the output of being <em>complex</em>. Because there's no value for the input, , that can make the output of <em>undefined</em> or <em>complex</em>, its Domain can be any number.
Domain:
Range:
In finding the Range, it is actually the same logic as finding the Domain but first, we'll have to do a bit of rewriting for the given function.
Let so .
First, we need to make the subject of the equation.
Making the subject:
.
In the Domain, we'll have to think of the value for the input, , that makes the output <em>undefined</em> or <em>complex</em>. In the Range, the same logic for the Domain, we'll have to think for the value of , that makes the <em>undefined</em> or <em>complex</em>. That's why we made in the equation the subject. In our rewritten equation, we can see that is under the <em><u>square</u></em> root. Which means if is negative, will be <em>complex</em>. So we have to make be greater than or equal to () so that won't be complex.
Solving for the inequality,
Range: