Question

Help with functions and domains?

so I need to find the domain of y= x² + 4 and I need the steps on how to approach it and I need it in "set builder notation." Thanks in advance!

Answer 1

domain means set of values, the 'x' variable can take.

x cannot take values which will make
1) denominator = 0
2) the quantity under square root sign as negative.

so what can u say about your x? which values it cannot take ?

Answer 2

So is it that is can take anything? (I'm sorry if that sounds really stupid. I was put in a high math class suddenly and I'm panicking since I have no idea what we're supposed to be reviewing XD)

Answer 3

you are correct!
since there is no denominator or square toot sign, your 'x' can take ANY REAL VALUE :)

now do u know how to write this in set builder notation ?

Answer 4

No idea! haha. Is it supposed to be {f(x)If(x)eR, f(x)=∞} ?

Answer 5

something like that only
{x| x \(\in\)R}

| ----->such that
\(\in\) ----> belongs to
R----> real number

Answer 6

Also, is that all I have to worry about when it comes to domain? Because my precalculus book makes it so confusing! It just goes in one ear and right out the other!

Answer 7

in most problems, yes, only 2 things, denominator and square root sign

Answer 8

\[y= \sqrt{x-5}\] So if I had that, would it me x
must be greater than 4?

Answer 9

whatever under sqrt sign > 0
so, x>5

because number like 4.99999.... will also make x-5 as negative...

Answer 10

oops, x \(\ge 5\)
because 5 will make it 0, which is allowed in domain :)

Answer 11

ahhh thank you very very much! does the y come in when I'm writing it in set builder notation
I'm so used to interval notation but my teacher strictly wants it set builder.

Answer 12

nopes, only,
doamin = {x|x \(\in\) R}

Answer 13

Thanks so much!

Answer 14

welcome ^_^