1
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
2
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
3
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
$${4 \over 9}$$
4
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
Let f : R $$\to$$ R be a function which satisfies
f(x + y) = f(x) + f(y) $$\forall$$ x, y $$\in$$ R. If f(1) = 2 and
g(n) = $$\sum\limits_{k = 1}^{\left( {n - 1} \right)} {f\left( k \right)}$$, n $$\in$$ N then the value of n, for which g(n) = 20, is :
A
20
B
9
C
5
D
4
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