JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

f: R \rightarrow R

satisfies

f(x+y)=f(x)+f(y)

\forall x, y \in R

and

f(1)=7

, then

\sum\limits_{{r=1}}^n f(r)

View answer and explanation

Correct option: D

\frac{7 n(n+1)}{2}

Option D (

\frac{{7 n(n+1)}}{{2}}

) is correct because the sum of the function values from 1 to n is derived using the given functional equation and the sum of the first n natural numbers.

More Questions from FUNCTIONS

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f:(-\infty, 2] \longrightarrow(-\infty, 4]

, where

f(x)=x(4-x)

, then

f^{-1}(x)

is given by: If

g(f(x))=|\sin x|

and

f(g(x))=(\sin \sqrt{x})^2

, then Let

f:\left( {2,\;3} \right) \to \left( {0,\;1} \right)

be defined by

f\left( x \right) = x - \left[ x \right]

, then

{f^{ - 1}}\left( x \right)

equals Let

f: R \rightarrow R

be defined as

f(x)=x^4

, Choose the correct answer. Which of the following functions are odd functions Let

f(x)=(x+1)^2-1(x \geq-1)

. Then the set

S=\left\{x: f(x)=f^{-1}(x)\right\}

contains