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Consider an arbitrary function \( f: X \rightarrow Y \) : It induces two important set mappings. If \( A \) is a subset of \( X \), then its image \( f(A) \) is the subset of \( Y \) defined by \( f(A)=\{f(x): x \in A\} \) Similarly, if \( B \) is a subset of \( Y \), then its inverse image \( f^{-1}(B) \) is a subset of \( X \) defined by \( f^{-1}(B)=\{x: f(x) \in \mathrm{B}\} \)
Let \( f(x)=-\log _{2} x+3 \) and \( A=[1,4] \) then \( f(A) \) is equal to
(a) \( [1,9] \)
(b) \( [1,2] \)
(c) \( [2,4] \)
(d) \( [1,3] \)
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