Let \( f \) be a one-one function with domain \( \{x, y, z\} \) and range \( \{1,2,3\} \). It is...

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Let \( f \) be a one-one function with domain \( \{x, y, z\} \) and range \( \{1,2,3\} \). It is given that exactly one of the following statements is true and the remaining two are false : \( f(x)=1 \), \( f(y) \neq 1, f(z) \neq 2 \) determine \( f^{-1}(1) \).
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