Question

true or false. the square root of x^2 = x is an identity

Answer 1

false

Answer 2

why

Answer 3

Because you the equation is not satisfied for every number you plug into it.

Answer 4

\[2^2\neq2\]

Answer 5

ohhh sorry. I did not see the square root. Wait

Answer 6

\[\sqrt{x^2}=x\]

Answer 7

yeah

Answer 8

is not and identity either.

Answer 9

why?

Answer 10

\[\sqrt{(-1)^2}\neq-1\]

Answer 11

Because the equation is not always true.

Answer 12

This is an identity:\[\sin^2\theta+\cos^2\theta=1\]

Answer 13

No matter what value of theta you choose. the equation is always true.

Answer 14

ok thanks. how about this question:
if f(x)=g(x) is an identity with domain of validity D, which of the following must be true?
a) for any x in D, fx is defined
b) for any x in D, gx is defined.
c) for any x in D, fx=gx
(you can choose all of them, two of them, one of them, none, etc whichever u think are true)

Answer 15

all of them are true.

Answer 16

in the case of your first question the domain of validity D = positive numbers and zero.

Answer 17

and then it is a identity.

Answer 18

ok thank you

Answer 19

You're welcome. By the way which course is this question from?

Answer 20

ohh ok. Have fun with that!