Fallacy!

Algebra Level 4

Let \(f:\{x,y,z\} \rightarrow \{a,b,c\}\) is an injective function.

It is known that only one of the following statements is correct and rest are false:

1). \(f(x) \ne b\)

2). \(f(y) =b\)

3). \(f(z) \ne a\)

What is \(f(x)\)?

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