Hi THis is for Trig/Pre-calc I was wondering how do you exactly do this. How to state the domain of each function and evaluate each function and state the domain.
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The first two have a domain of `the set of all real numbers`. We can plug in any real number for x and get some number for y. There are no division by zero errors to worry about. We also don't have to worry about taking the square root of a negative number.
However, the third one will have a division by zero error. Do you see which x values cause the denominator to be zero?
Which first two?
I have the answers to these questions already that my teacher gave me already,but I just not sure how exactly how he got these answers.
On domain problems, you always want to first look for what's illegal and excluding those out.
From looking at your test review, you have 2 main things:
1) 1/0 ........is illegal and are not in the realm of real numbers!
2) squareroot of a negative...... is illegal and not in the realm of real numbers!
So any numbers that make those two things happen cannot be in your domain.
Otherwise everything else that evaluates to the value IS in your domain.
Hope that helps!
oops 1) is just dividing by zero, not just 1/0
So anything 0 or square root of a negative is not a real number?
Also for number 3 is this the right reason that it gives the function an undefined answer makes x not equal to 2?
Anything divided by zero is not a real number, because division by zero is not defined.
And square root of a negative is not a real number.
(But ends up being useful later as an "imaginary number")
Ohh okay so divided by zero is not a real number. That makes sense.