Question

how do i do x \mapsto \frac{1}{\sqrt{3 x+13}}?

Answer 1

what is mapsto?

Answer 2

\[x\mapsto\frac{1}{\sqrt{3x+13}}\]

Answer 3

what is the qestion?

Answer 4

I'm sorry. I have no idea, I just copy pasted the equation. I have to find the domain of the function {1}{\sqrt{3 x+13}}?

Answer 5

ahh
so we cant divide by 0, and we cant take the square root of a negative number
so we have to make sure both of these dont happen

we can do this buy finding out what x's make this a true statement 3x+13>0
do you understand why?

Answer 6

why?

Answer 7

well if we let a = 3x+13
we have \[\frac{1}{\sqrt{a}}\]now it should be easy to see why we need a to be greater than 0, and why a cant be 0

do you why a>0 is a must?

Answer 8

yes

Answer 9

ok so we said the thing in the square root, which is in the denominator must be greater than 0
so
3x+13 must be > 0

Answer 10

okay

Answer 11

you will basiccally have 3 problems with domain
1) square root of negative numbers
2) dividing by 0
3) taking log of non positive numbers

Answer 12

basically*

Answer 13

in this example you had both 1) and 2)

Answer 14

okay

Answer 15

when I find domain, I dont look for things that x CAN be, I look for things x CANT be.

Answer 16

thanks!

Answer 17

np