AIEEE 2003 | Functions Question 135 | Mathematics

A function $$f$$ from the set of natural numbers to integers defined by $$$f\left( n \right) = \left\{ {\matrix{ {{{n - 1} \over 2},\,when\,n\,is\,odd} \cr { - {n \over 2},\,when\,n\,is\,even} \cr } } \right.$$$ is

neither one -one nor onto

one-one but not onto

onto but not one-one

one-one and onto both

AIEEE 2003

MCQ (Single Correct Answer)

-1

If $$f:R \to R$$ satisfies $$f$$(x + y) = $$f$$(x) + $$f$$(y), for all x, y $$ \in $$ R and $$f$$(1) = 7, then $$\sum\limits_{r = 1}^n {f\left( r \right)} $$ is

$${{7n\left( {n + 1} \right)} \over 2}$$

$${{7n} \over 2}$$

$${{7\left( {n + 1} \right)} \over 2}$$

$$7n + \left( {n + 1} \right)$$

AIEEE 2003

MCQ (Single Correct Answer)

-1

Domain of definition of the function f(x) = $${3 \over {4 - {x^2}}}$$ + $${\log _{10}}\left( {{x^3} - x} \right)$$, is

(-1, 0)$$ \cup $$(1, 2)$$ \cup $$(2, $$\infty $$)

(1, 2)

(-1, 0) $$ \cup $$ (1, 2)

(1, 2)$$ \cup $$(2, $$\infty $$)