Hi ash4gmat,
While this question might look a little 'weird', it's just asking us to deal with a function. In real basic terms, functions are just a different way to write a line formula. For example...
Y = 2X + 1
f(X) = 2X + 1
These two equations 'mean' the same thing. Here's how each would look if we plugged in X = 3:
Y = 2(3) + 1 = 7
f(3) = 2(3) + 1 = 7
That having been established, we're told that X is POSITIVE. We're asked if the f(X^2) = f(X)^2. This is a YES/NO question.
1) f(X) = Sqrt(X)
This tells us what math to do when we use the function. Now we have to determine whether f(X^2) = f(X)^2 or not...
As an example, let's TEST X=1
f(1^2) = f(1) = Sqrt(1) = 1
f(1)^2 = [Sqrt(1)]^2 = 1^2 = 1
1 = 1, so the answer to the question is YES.
As another simple example, let's TEST X=4
f(4^2) = f(16) = Sqrt(16) = 4
f(4)^2 = [Sqrt(4)]^2 = 2^2 = 4
4 = 4, so the answer to the question is YES.
At this point, you should recognize a pattern. We're squaring a number and then square-rooting it OR we're square-rooting it and then squaring it. Squaring and square-rooting are "opposites", and since we're dealing with positive numbers only, they 'cancel out' and the values of f(X^2) and f(X)^2 will always be the same: X. The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.
2) X=9
This tells us NOTHING about how the function 'works', so there's no way to answer the question.
Fact 2 is INSUFFICIENT.
Final Answer: A
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Function-data sufficiency
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Given: x > 0ash4gmat wrote:Please help:
Q:If x>0, does
f(x^2)=f(x)^2?
(1) f(x)=Sqrt.x
(2)x=9
Required: Is f(x^2) = f(x)^2 ?
Statement 1: f(x) = √x
f(x^2) = √(x^2) = x
f(x)^2 = (√x)^2 = x
SUFFICIENT
Statement 2: x = 9
We do not know anything about the function f(x)
Hence we cannot comment on the relation.
INSUFFICIENT
Correct Option: A
S1:
f(x²) = (√x)²
f(x) * f(x) = √x * √x
Since (√x)² = √x * √x, we DO have f(x²) = f(x)², so this is sufficient.
S2:
This gives us f(81) and f(9)*f(9) ... but we don't know what the function does!
f(x²) = (√x)²
f(x) * f(x) = √x * √x
Since (√x)² = √x * √x, we DO have f(x²) = f(x)², so this is sufficient.
S2:
This gives us f(81) and f(9)*f(9) ... but we don't know what the function does!
