Find \( f^{-1}(9) \) if \( f(x)=x^2 \)
Question:
If \( f : Q \to Q \) is defined as \( f(x)=x^2 \), then \( f^{-1}(9) \) is equal to
(a) \(3\)
(b) \(-3\)
(c) \(\{-3,3\}\)
(d) \(\phi\)
Solution:
\( f^{-1}(9) \) means the set of all rational numbers whose image is \(9\).
So,
\[ x^2=9 \]
\[ x=\pm 3 \]
Therefore,
\[ f^{-1}(9)=\{-3,3\} \]
\[ \boxed{\text{Correct Answer: (c)}} \]