Functions
Counting functions satisfying a constraint
MJMT_Full_Test_11
Grade 12
Question:
If $f:\{1,2,3,4\}\to\{1,2,3,4\}$ is a function such that $|f(\alpha)-\alpha|\leq 1$ for $\alpha\in\{1,2,3,4\}$, then total number of such functions is
Step-by-Step Solution
Key Concept: For each $\alpha$, count the valid values of $f(\alpha)$ satisfying $|f(\alpha)-\alpha|\leq 1$ within the codomain $\{1,2,3,4\}$. Multiply independent counts.
Total cases $= 2 \times 3 \times 3 \times 2 = 36$.
Correct Answer: 2