JEE MATHEMATICS MCQ: FUNCTIONS

1 Hard

1 of 1

Application +4 | -1

Let

f: \mathbb{R} \rightarrow \mathbb{R}

be a function such that

f(x+y)=

f(x)+f(y)

for all

x, y

belonging to

\mathbb{R}

. If

m

and

n

are integers, then

f(m / n)

is equal to

View answer and explanation

Correct option: C

\left(\frac{m}{n}\right) f(1)

Option C (

\left(\frac{{m}}{{n}}\right) f(1)

) is correct because it follows from the given functional equation

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

and properties of integers and rational numbers.

More Questions from FUNCTIONS

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

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

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

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

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

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

f: R \rightarrow R

f(x)=x^4

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

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