1
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
Let N be the set of natural numbers and two functions f and g be defined as f, g : N $$\to$$ N such that

f(n) = $$\left\{ {\matrix{ {{{n + 1} \over 2};} & {if\,\,n\,\,is\,\,odd} \cr {{n \over 2};} & {if\,\,n\,\,is\,\,even} \cr } \,\,} \right.$$;

and g(n) = n $$-$$($$-$$ 1)n.

Then fog is -
A
neither one-one nor onto
B
onto but not one-one
C
both one-one and onto
D
one-one but not onto
2
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
Let A = {x $$\in$$ R : x is not a positive integer}.

Define a function $$f$$ : A $$\to$$  R   as  $$f(x)$$ = $${{2x} \over {x - 1}}$$,

then $$f$$ is :
A
not injective
B
neither injective nor surjective
C
surjective but not injective
D
injective but not surjective
3
JEE Main 2019 (Online) 9th January Morning Slot
+4
-1
For $$x \in R - \left\{ {0,1} \right\}$$, Let f1(x) = $$1\over x$$, f2 (x) = 1 – x

and f3 (x) = $$1 \over {1 - x}$$ be three given

functions. If a function, J(x) satisfies

(f2 o J o f1) (x) = f3 (x) then J(x) is equal to :
A
f1 (x)
B
$$1 \over x$$ f3 (x)
C
f2 (x)
D
f3 (x)
4
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
Let f : A $$\to$$ B be a function defined as f(x) = $${{x - 1} \over {x - 2}},$$ Where A = R $$-$$ {2} and B = R $$-$$ {1}. Then   f   is :
A
invertible and $${f^{ - 1}}(y) =$$ $${{3y - 1} \over {y - 1}}$$
B
invertible and $${f^{ - 1}}\left( y \right) = {{2y - 1} \over {y - 1}}$$
C
invertible and $${f^{ - 1}}\left( y \right) = {{2y + 1} \over {y - 1}}$$
D
not invertible
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