Question

Let $f$ be a non-zero real valued continuous function satisfying $f(x+y)=f\left(x\right).f\left(y\right)$ for all $x,y$ $ϵ$ $R$. If $f\left(2\right)=9$ then $f\left(6\right)=$

• A. $3^2$
• B. $3^6$
• C. $3^4$
• D. $3^3$

Answer 1

The correct option is B $3^6$

$f(x+y)=f\left(x\right).f\left(y\right)$

$f\left(4\right)=f\left(2\right).f\left(2\right)$ satisfying this relation

$f\left(4\right)=f(2{)}^2$

$f\left(6\right)=f\left(4\right).f\left(2\right)=f(2{)}^3$

$=9^3$

$=(3{)}^6$