Question

Can someone explain this to me? I can't seem to understand range or domain... :(
Determine the domain of the function.
f(x)=1-x (The 1-x is under a square root sign.)

All real numbers
x > 1
x ≤ 1
All real numbers except 1

Answer 1

hint: you cannot take the square root of a negative number

Answer 2

Can you find the solution with the given hint?

Answer 3

Well, first I put x>1, but that was wrong. Are negative numbers concidered real?

Answer 4

negative numbers are real

but taking the square root of a negative number results in a non-real number

Answer 5

So what you have to do is force 1-x to be 0 or positive

Answer 6

Also, if you has something like this,
\[\sqrt{P(x)}\]
You must impose the condition,
\[P(x)\geq0\]
In your case, you should solve,
\[1-x\geq0\]

Answer 7

Wait, so if I chose x is less than or equal to 1, then when it subtracted, it would be the opposite, so it would be positive... Right? I apologize. Math is my best subject, but I don't remember studying range or domain...

Answer 8

Yes, now you are right.

Answer 9

Awesome. Thanks. I'll probably be back. :p

Answer 10

May the luck be with you! ;)

Answer 11

:) God bless!