Hi i'm having some trouble explaining one thing.
This is what's written in my practice questions. Can someone help my explain this.We know x=2 and x=4 are the only solutions to f(x)= 0. Solve the equations f(4x) = 0 - Please explain!
The teacher said it was pretty simple once you figured it out.
@ masters : but huuum... we do not know if f is a polynomial... and actually, if x=2 and x=4 and f a polynomial, then f(x)=a(x-2)(x-4) where a is a non-zero constant.
@ the OP :
"x=2 and x=4 are the only solutions to f(x)=0" this can be rewritten :
So to the solution f(4x), let for more convenience and less confusing (it doesn't change anything if we call x t or whatever) :
From the first equivalence, we have
That is to say , that is to say