Hi,
Question from SAT Subject Test Math 2. Hope you can answer it.
If f(x)=sqrt (x^2), then f(x) can also be expressed as:
A. x
B. -x
C. +/- x
D. modulus x
E. f(x) cannot be determined because x is unknown.

My answer was A, but the given answer is C. Could you please explain?

The best way to explain, I think, is to point out what happens when x = –2:

So f(–2) = 2. In other words, when x = –2, then f(x) = –x.  Of course, f(2) is ALSO equal to 2, so f(x) can also just be equal to x.

That’s why you have to say f(x) = ±x.