Question

$f$ $:R\to R$ such that $f(x+f(x\left)\right)=4f\left(x\right)$ and $f\left(1\right)=4$. What is the value of $f\left(5\right)$?

Answer 1

Given, $f\left(1\right)=4$

We have $f(x+f(x\left)\right)=4\left(fx\right)$

Put $x=1$

Therefore, $f(1+f(1\left)\right)=4f\left(1\right)$

$\Rightarrow f(1+4)=4\left(4\right)$

$\Rightarrow f\left(5\right)=16$