## Function f(x) satisfies f(x) = f(x^2) - PS (>700)

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### Function f(x) satisfies f(x) = f(x^2) - PS (>700)

If a function f(x) satisfies $f(x) = f(x^2)$ for every 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) $f(0) = 0$
respuesta: show

Luke
Mensajes: 258

### Re: Function f(x) satisfies f(x) = f(x^2) - PS (>700)

This question can be a bit tricky!

I tried by using examples, but we must be careful because the equality is valid for every x, so you can't use any function to check the options!

However, we can write down several equations to facilitate the checking option by option, for example:
f(4)=f(16)
f(2)=f(4)
f(-2)=f(4)
f(1)=f(1)
f(0)=f(0)
f(3)=f(9)

With that we can easily rule out the third last options. We can also rule out option A, because f(4)=f(2) <> f(2)*f(2). Then, option B is correct (f(-2)=f(4)=f(16))