Question

The number of functions that can be defined from $A=\{-1,0,1\}$ to $B=\{2,7,8,9\}$ is

• A. $24$
• B. $12$
• C. $81$
• D. $64$

Answer 1

The correct option is D $64$

The set $A$ has 3 elements and $B$ has 4 elements

Now, each element in $A$ has four choices to be mapped to. Each such choice gives you a unique function.

Since each element in $A$ has 4 choices, the total number of functions from $A$ to $B$ is given as : $4\times 4\times 4$

Therefore, total number of functions $=4\times 4\times 4=64$.

Hence, the number of functions that can be defined from $A$ to $B$ is $64$.