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.