$f: X \to X$

Algebra Level 2

For set $X=\{-3, 0, 3\},$ how many functions $f: X \to X$ exist such that $\left(f(-3)+3\right) \times \left(f(3)-3\right) \neq 0?$

27 18 24 12

1 solution

Vishnu Pitty
Apr 20, 2014

According to the expression given, f(-3) must equal either 3 or 0 and f(3) must equal either -3 or 0 since neither of the two factors of the given expression can equal 0. This gives us two possible mappings each for the functions f(3) and f(-3). For f(0), all three values of 3,0 and -3 are possible. Hence for f(0) we have three possible mappings.

Thus, for an existing function "f" on X = {3,0,-3}, there will be a total of 2x2x3 combinations = 12 combinations.

Hence 12 is the answer.

f : X → X f: X \to X f : X → X

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$f: X \to X$