1
JEE Main 2021 (Online) 25th February Morning Shift
+4
-1
Let f, g : N $$\to$$ N such that f(n + 1) = f(n) + f(1) $$\forall$$ n$$\in$$N and g be any arbitrary function. Which of the following statements is NOT true?
A
If g is onto, then fog is one-one
B
f is one-one
C
If f is onto, then f(n) = n $$\forall$$n$$\in$$N
D
If fog is one-one, then g is one-one
2
JEE Main 2021 (Online) 24th February Morning Shift
+4
-1
Let f : R → R be defined as f (x) = 2x – 1 and g : R - {1} → R be defined as g(x) = $${{x - {1 \over 2}} \over {x - 1}}$$. Then the composition function f(g(x)) is :
A
one-one but not onto
B
onto but not one-one
C
both one-one and onto
D
neither one-one nor onto
3
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
For a suitably chosen real constant a, let a

function, $$f:R - \left\{ { - a} \right\} \to R$$ be defined by

$$f(x) = {{a - x} \over {a + x}}$$. Further suppose that for any real number $$x \ne - a$$ and $$f(x) \ne - a$$,

(fof)(x) = x. Then $$f\left( { - {1 \over 2}} \right)$$ is equal to :
A
$${1 \over 3}$$
B
–3
C
$$- {1 \over 3}$$
D
3
4
JEE Main 2020 (Online) 6th September Morning Slot
+4
-1
If f(x + y) = f(x)f(y) and $$\sum\limits_{x = 1}^\infty {f\left( x \right)} = 2$$ , x, y $$\in$$ N, where N is the set of all natural number, then the value of $${{f\left( 4 \right)} \over {f\left( 2 \right)}}$$ is :
A
$${2 \over 3}$$
B
$${1 \over 9}$$
C
$${1 \over 3}$$
D
$${4 \over 9}$$
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