Question

how do i state the domain for these functions?
1. f(x) = 3x / x^2-5


2. h(x)= x+2 / √x^2-7

Answer 1

\[\frac{ 3x }{ x^2-5 }\]?

Answer 2

\[h(x)=\frac{ x+2 }{ \sqrt{x^2-7} }\]?

Answer 3

@wagnermar use more parenthesis please, as you would in a calculator.

Answer 4

@Johnbc yes thats correct.
@zzr0ck3r sorry

Answer 5

Yes it's correct

Answer 6

?

Answer 7

what is correct?

Answer 8

The posted replies are correct.

Answer 9

yes, it's correct.

Answer 10

do you know how to solve these problems? i need help

Answer 11

Sorry ma'm. I am really sorry. Please excuse me.

Answer 12

ok...

Answer 13

the domains of the functions are the values of the independant variable for which the functions are defined. can you tell me when the first function is not defined.

Answer 14

x^2-5 ?

Answer 15

Here's a hint; an expression is undefined when you divide by zero.

Answer 16

x^2-5=0?

Answer 17

Exactly. Now you need to solve for x. This tells us what x-value the function is not defined for. Because when x is this soon-to-be-found value, you are dividing by zero, which is undefined.

Answer 18

x^2=5

Answer 19

Yupp.... keep on going. You haven't solved for x yet. You are done when you have\[x=some-expression\]

Answer 20

x=√5 and x=-√5 ?

Answer 21

Correct. Therefore, the first function is defined whenever x is not \[\pm \sqrt{5}\]That means the domain would be all real numbers except plus or minus square root of 5.

Answer 22

ok

Answer 23

The other function is not defined when the denominator is zero, but it also has another limitation. Do you know what that is?

Answer 24

??? ≠ ??? i dont know?

Answer 25

What is the square root of a negative number?

Answer 26

Trick question. The square root of a negative number is undefined.

Answer 27

a square root of a negative number isnt possible right?

Answer 28

Correct. Therefore, the function is only defined when x squared minus seven is greater than zero.

Answer 29

ok