how do i know what the domain is in these problems...

Question

i know that domain is the x value but how can i tell what it is?

y=1/x
y=3/x^2-49
y{x}
y=square root of 3-x
y=[x].

Answer 1

in plain English, the domain is the value of x that you may use in your given function to return a value

in your first one, remember that we cannot divide by zero, so x=0 is the only value which would not work

so the domain would be the set of real numbers, except x is not equal to zero

for your second, y = 3/(x^2-49)
the trouble arises when x = ± 7

do you think you can state the domain?

another case where difficulty arises is when your function tries to take the square root, (or any even root) of a negative number.

e.g. your third one:
y = √(3-x)

your domain would be all real values of x which would make (3-x) ≥ 0

Answer 2

i have a question.... when i get a function, how do i konw if it has an inverser... for example, y=ab.solute value x, then -2. i plugged in x=ab.solute val. of y, then -2. but how do i know if that is an inverse??