alihong2010 wrote:
Given 1/2f(x)=f(x/2), which of the following is true for all values of f(x)?
A.f(x)=2x+2
B.f(x)=13x
C.f(x)=x^2
D.f(x)=x-10
E.f(x)=sqrt(x-4)
I know the answer is B and I got it by trying each f(x) function. However the answer indicates, "the fastest method is to use logical: since the order of operations says that order does not matter with multiplication and division but does matter between multiplication and addition/subtraction, or multiplication and exponents, choose a function that has only multiplication and/or division."
Could anyone explain this logic? Thank you.
well, since the problem features transformations which feature multiplication (1/2*f(x)) and division (x/2), it's safe to say that the DM part of PEDMAS is used- I guess that leads to trying only equations with DM transformations? I'm not 100% sure either