Question

 The number of constant functions possible from \[\mathbb{R}\] to B $ = \left\{ {2,4,6,8, \cdots ,24} \right\}$ is
A.24
B.12
C.8
D.6

Answer 1

Hint: As we all know for any value constant function gives the same output. So here for any element of \[\mathbb{R}\], we have the same value from B. Here B contains 12 elements so the number of constant functions possible from \[\mathbb{R}\] to B is 12.

Complete step-by-step solution:
For a constant function from \[\mathbb{R}\] to B, x should be related to only one element in B.
\[\because \]B $ = \left\{ {2,4,6,8,10,12,14,16,18,20,22,24} \right\}$
⇒ B contains 12 elements.
 Thus, the number of constant functions possible from \[\mathbb{R}\] to B =$\left\{ {2,4,6,8, \cdots ,24} \right\}$ is 12.
Hence, Option B. 12 is the correct answer.

Note: A constant function is a function whose (output) value is the same for every input value.
Example: function \[f\left( x \right) = 4\] here \[f\left( x \right)\] is a constant function because of that for any value of x answer will be 4.
 In general, we can say that the total number of constant functions from set A (containing n elements) to set B (containing m elements) is the number of elements in set B i.e. m.