JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Analyzing +4 | -1

Let

A = \{ 1,\,\,2,\,\,3,\,\,...,\,\,10\}

and

f:A \to A

be defined as

f(k) = \left\{ \begin{array}{l} k + 1,\quad if\,\,k\,\,is\,\,odd\\ k,\quad {\kern 1pt} {\kern 1pt} \quad if\,\,k\,\,is\,\,even \end{array} \right.

Then, the number of possible functions

g:A \to A,

such that

gof = f

View answer and explanation

Correct option: A

{10^5}

Option A is correct. The number of possible functions

g

is found by recognizing that

g(x) = x

for even

x

, and for odd

x

g(x)

can take any value in

A

, leading to

10^5

possibilities.

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