Question

If f : R → R is defined by f(x) = x², find f⁻¹ (−25).

Answer 1

$$\begin{gathered} \text{Let}{f}^{-1}\left(-25\right)=x \\ \Rightarrow f\left(x\right)=-25 \\ \Rightarrow x^2=-25 \\ \text{We cannot find}\mathit{\text{x∈R,}}\mathrm{such}\mathrm{that}{\mathrm{x}}^2=-25\left({\text{as x}}^2\text{≥0 for all x∈R}\right) \\ \mathrm{So},f^{\mathit{-}\mathit{1}}\left(\mathit{-}\mathit{25}\right)\mathit{=}\varphi \end{gathered}$$