Problem Solving

Function F(x) satisfies F(x) = F(x^2) for all x. Which of the following must be true

F(4) = F(2)*F(2)
F(16) - F(-2) = 0
F(-2) + F(4) = 0
F(3) = 3*F(3)
F(0) = 0

f(x)=f(x^2) (neat function )

A)f(4)=f(2)*f(2) not true, beacuse f(4) = f(2) (and also = f(16) and f(-2)) so f(4) can't be the same as f(2)*f(2)

B) f(16)-f(-2) = 0 true, as i stated above f(4)=f(16) (16=4^2) and f(4) is also equal to f(-2) (4=(-2)^2) so f(16)-f(-2) is the same as f(4)-f(4) and that would indeed equal 0.

Answer is B.
what is the OA?

Function F(x) satisfies F(x) = F(x^2) for all x.

F(4) = F(2)*F(2)
LHS:
F(4) = 4^2 = 16
RHS:
F(2)*F(2) = 2^2 * 2^2 = 4*4 = 16
RHS=LHS

So should the answer not be the first choice - F(4) = F(2)*F(2) ?

don't confuse f(4) with 4, you don't know the result of f(4), you only know that it has the same value as f(4^2) or f(2^2)

agps wrote:don't confuse f(4) with 4, you don't know the result of f(4), you only know that it has the same value as f(4^2) or f(2^2)

Risht OA is B. Thanks for the expln