bhumika.k.shah wrote:if function f(x) satisfies f(x)=f(x^2) for all x , which of the following must be true?

A. f(4) =f(2) f(2)
B. f(16)-f(-2) = 0
C. f(-2)+f(4)=0
D.f(3)=3f(3)
E.f(0)=f(0)

OA B

I used first value to find out its square and accordinly solved each option ...
i thought it was either A or E
but in reality it was B
just my luck!

How about if we try to find some function, f(x) such that f(x) = f(x^2)
This might help us eliminate some answer choices.

Here's a function that satisfies the initial requirement: f(x) = 3
So, f(2) = 3 and f(2^2)=3

If we use this function to check each answer choice, we can eliminate A, C and D.

At this point, we have to recognize that E must be true. We are saying some value (f(0))equals itself (f(0)). Hard to argue against that.

Also, ajith's explanation . . .
f(x)=f(x^2)
f(-2) = f(4)
f(4) = f (16)
Hence f (16) - f (-2) = 0
. . . demonstrates that B is also correct.

So, I'd say that we appear to have two correct answers (B and E)

What's the source?