Question

How do I find the domain of the function?
g(x)=sqrt(x+1)

Answer 1

the domain are the "legal" or "allowed" x values.

you assume the domain is all real numbers (-infinity to +infinity)
then exclude numbers that "cause problems" if you use them in your equation

You do not any divide by zero
You do not want any square roots of a negative number.

Answer 2

your equation has no division, so no need to worry about divide by zero

however, you might end up with square root of a negative number for some numbers
we must not allow those in the domain

Answer 3

in other words, you want
x+1 (the thing inside the square root) to be 0 or bigger
x+ 1 ≥ 0

can you figure out what the domain is ?

Answer 4

I do not understand these at all.

Answer 5

which part?

do you understand we don't want square root of a negative number ?

Answer 6

So I want to get the number inside of the radical bigger than 0. how do I do that? I understand that you don't want to do the sqrt of a negative.

Answer 7

if you have
sqrt(x)
x cannot be negative. we show this by saying x must be 0 or bigger
(x can be 0, because sqr(0) = 0 works)

so the domain is x is 0 or bigger
that is the answer, but you should learn how to write it using "math"

we would write x ≥ 0
we put x next to the "big" side of > and 0 next to the "little" end of > to show x is bigger than 0. we write a line underneath the > to get ≥ to show x could also be 0

Answer 8

for your problem
sqr(x+1)

we want the "stuff" inside the square root to be 0 or bigger.
we want

x+1 is 0 or bigger
or
x+1 ≥ 0
normally, we would re-write this by add -1 to both sides
x+1 - 1 ≥ 0 -1

on the left side +1-1 simplifies to 0 and x+0 is x
x ≥ -1
is the "nice" way to write it.
it means x must be -1 or bigger.

Answer 9

Ok I got that. So on my next problem if I have f(t) sqrtcubed(t+4) I would get the thing inside the sqrt to be bigger than 4. How do these work when the sqrt is cubed?

Answer 10

Is that cube root...? take a screenshot and upload it.

Answer 11

yes a cube root. Idk how to take a screen shot? lol

Answer 12

Cube root does NOT have to be greater than zero. You can cube root a negative number. Cube roots domain is all real numbers.

Answer 13

so (- infinity,infinity)?

Answer 14

" sqrtcubed(t+4) I would get the thing inside the sqrt to be bigger than 4"

BUT if it was sqrt(x+4) you'd write:
x+4 ≥ 0

Yes, that's right, your domain

Answer 15

Thank you!

Answer 16

do you mean

Answer 17

yes.

Answer 18

Then yes the domain is as you said (- infinity,infinity)