Question

Suppose f is a real function satisfying $f(x+f(x\left)\right)=4f\left(x\right)$ and $f\left(1\right)=4$. Find the value of $f\left(21\right)$.

• A. $16$
• B. $64$
• C. $21$
• D. $80$

Answer 1

Answer: (B)

$64$

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

Substituting $X=1$ we get $f(1+f(1\left)\right)=4f\left(1\right)\Rightarrow f(1+4)=16\Rightarrow f\left(5\right)=16$

Now substitute $x=5$, $f(5+f(5\left)\right)=4f\left(5\right)\Rightarrow f(5+16)=64=f\left(21\right)$