If x > 0, does f(x^2) = f(x)^2 ? (1) f(x) = x (2) x = 9

Question : does f(x^2)=f(x)^2?

Statement 1:f(x) = √x

i.e. f(x)^2 = (√x)^2 = x

and i.e. f(x^2) = √(x^2) = x

i.e. f(x^2)=f(x)^2

SUFFICIENT


Statement 2:x=9

But we do NOT have the function to solve and check what question expects us to check hence

NOT SUFFICIENT


Answer: option A

nahid78 : Please post DS question in DS forum

Bunuel : Please shift the question in DS forum

Sorry for bumping this old thread, but I have the same problem here, isn't the Sqrt(x^2) = |x| and hence it won't be equal to x?

Bunuel can you help please?

Notice that the question says that x is positive: If x > 0...

For positive x, |x| = x.

Step 1: Analyse Question Stem


x is greater than zero.
We have to find if f(\(x^2\)) = \(f(x)^2\)

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1: f(x) = √x

f(\(x^2\)) = \(\sqrt{x^2} \)

On the GMAT, \(\sqrt{x^2}\) = |x|; this means that these are equivalent functions, taking the same inputs and giving the same outputs. Therefore,

\(\sqrt{x^2}\) = x if x ≥ 0
= -x if x < 0

Since the question data clearly says that x > 0, f(\(x^2\)) = \(\sqrt{x^2}\) = x.

\([f(x)]^2\) = \([\sqrt{x}]^2\) = x

Therefore, f(\(x^2\)) = \(f(x)^2\)

The data in statement 1 is sufficient to answer the question with a definite YES.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.

Statement 2: x = 9

We have no information about the definition of the function and therefore, a value of x is of no use in answering the question.

The data in statement 2 is insufficient to answer the question with a YES or NO.
Statement 2 alone is insufficient. Answer option D can be eliminated.

The correct answer option is A.