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Question
If f : R → R is defined by f(x) = x2, find f−1 (−25).
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Solution
\[Let f^{- 1} \left( - 25 \right) = x\]
\[ \Rightarrow f\left( x \right) = - 25\]
\[ \Rightarrow x^2 = - 25\]
\[\text{We cannot find x } \in R,\text{such that} x^2 = - 25 \left( \text{ as x}^2 \geq0 \text{ for all } x \in R \right)\]
\[So, f^{- 1} \left( - 25 \right) = \phi\]
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