Question

Find the domain of the following functions

Answer 1

\[f(x)=\frac{ \sqrt{x+2} }{ x-5 }\]

Answer 2

\[g(x)=\frac{ x-3 }{ \sqrt{x-1}}\]

Answer 3

how far did you get with any of these?

Answer 4

not far at all

Answer 5

like i need helpppp i haves so much work to do and so lil time, i dont wanna be up all nite...

Answer 6

well first off, hopefully you see that x-5 in the denominator cannot be zero, so x-5 = 0 leads to x = 5

if x = 5, then the denominator x-5 is 0

that means x = 5 is NOT part of the domain

Answer 7

agreed so far?

Answer 8

yes

Answer 9

in the numerator of f(x), we have a radical

you cannot take the square root of a negative number, so x+2 cannot be negative

x+2 is either 0 or positive

solve \[\Large x+2 \ge 0\] for x. Tell me what you get

Answer 10

x greater or equal to -2

Answer 11

yes

Answer 12

oh wait, i already solved for this one. i need help with the second

Answer 13

so x cannot be 5
AND
x has to be greater than or equal to -2

Answer 14

same idea with g(x)

you cannot divide by 0 and you cannot take the square root of a negative number

Answer 15

what makes the denominator of g(x) equal to 0 ?

Answer 16

3 cant be an option

Answer 17

why not?

Answer 18

because the top

Answer 19

you subtract -3

Answer 20

i mean add

Answer 21

right?

Answer 22

you can have 0 in the numerator though

Answer 23

what do you get when you solve sqrt(x-1) = 0 for x?

Answer 24

1

Answer 25

so if x = 1, then the whole denominator turns to 0

which is why x = 1 is NOT part of the domain

Answer 26

also, you need to ensure that x-1 is never negative

Answer 27

okay

Answer 28

and the other part?

Answer 29

solve x-1 >= 0 for x to get what?

Answer 30

1

Answer 31

x = 1 ? or x <= 1 ? or x >= 1 ?

Answer 32

x greater than 1

Answer 33

greater than or equal to 1, yes

Answer 34

oh wait, nvm the "or equal to" part

Answer 35

x cannot equal 1 because it leads to a division by zero error

Answer 36

okay

Answer 37

so? explaiiiin im confused tell me how to solve

Answer 38

you just said it: the domain is x > 1

Answer 39

any number larger than 1 will work as an input

if x = 1 or smaller, then you run into problems

Answer 40

okay
so the answer is x is not one and x is greater than 1?

Answer 41

saying x > 1 implies that x is not equal to 1

Answer 42

you don't need to say them both if you just say x > 1

Answer 43

okay, so thats the answer tho

Answer 44

yes

Answer 45

thnxxxx

Answer 46

no problem