+0 A function f randomly assigns values to f(1),f(2),f(3), and f(4) from the set {1,2,3,4} with replacement. What is the probability that f(f(x))=f(f(f(x))) for each in the set {1,2,3,4}? Express your answer as a common fraction.
0 So, here is my best shot:
Let \(f(f(x)=y\) and \(y\in {1,2,3,4}\)
Therefore:
\(f(f(x))=f(f(f(x)))\) becomes \(y=f(y)\)
This means we just need to find the probability of \(f(x)=x\) and the value of \(f(f(x))\) can be anything, it doesnt matter.
Thus, the probability of
\(f(x)=x\) where \(x\in {1,2,3,4}\)
\(= \boxed{\frac{1}{4}}\)
hope its right ngl
