$ x,y \in\mathbb{R}$ and $f:\mathbb{R} \rightarrow \mathbb{R}$, find a function that,
$$f(2x+(f(y)+f(f(y))=4x+8y$$
A) $f(x)=2^x$
B) $f(x)=2x$
C) $f(x)=2^x-3$
D) $f(x)=2x^2-3$
E) $f(x)=4x-2$
My problem is,it seems to me that there's something wrong with brackets. Or do I think wrong?
Looks like the red parenthesis is superfluous: $$f(2x+\color{red}{(}f(y)+f(f(y))=4x+8y$$ since $$f(y)+f(f(y)) = \color{red}{(}f(y)\color{red}{)}+f(f(y)) = \color{red}{(}f(y)+f(f(y))\color{red}{)},$$ so let us just ignore it.
That leaves us with three cases:
I believe the correct one should be 2., since it's the only one that one of the proposed solutions works for.