Let $f:R \to R$ be a function which satisfies $f\left( {x + y} \right) = f\left( x \right) + f\left( y \right)\forall x,\,\,\,y \in R.\,\,$ If $f\left( 1 \right) = 2$ and $g\left( n \right) = \sum\limits_{k = 1}^{\left( {n - 1} \right)} {f\left( k \right)}, $ $n \in N,$ then the value of $n,$ for which $g\left( n \right) = 20$ is

JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Application +4 | -1

Let

f:R \to R

be a function which satisfies

f\left( {x + y} \right) = f\left( x \right) + f\left( y \right)\forall x,\,\,\,y \in R.\,\,

f\left( 1 \right) = 2

and

g\left( n \right) = \sum\limits_{k = 1}^{\left( {n - 1} \right)} {f\left( k \right)},

n \in N,

then the value of

n,

for which

g\left( n \right) = 20

View answer and explanation

Correct option: A

The correct answer is A (5) because it is the value of n that satisfies the given functional equation and summation condition.