Question

If $f$ is a real valued function such that $f\left(x+y\right)=f\left(x\right)+f\left(y\right)$ and $f\left(1\right)=5$, then the value of $f\left(100\right)$ is

• A. $200$
• B. $300$
• C. $350$
• D. $400$
• E. $500$

Answer 1

The correct option is E

$500$

Finding the value :

Given,

$f\left(1\right)=5$

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

If $x=1,y=1$

$f\left(2\right)=2f\left(1\right)=2\times 5=10$

If $x=2,y=1,$

$f\left(3\right)=f\left(2\right)+f\left(1\right)=3f\left(1\right)=15$

$f\left(n\right)=nf\left(1\right)$

$f\left(100\right)=100\times f\left(1\right)=100\times 5=500$

Hence ,option E is correct