Question

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

Answer 1

$$\begin{gathered} \text{Let}{f}^{-1}\left(25\right)=x...\left(1\right) \\ \Rightarrow f\left(x\right)=25 \\ \Rightarrow x^2=25 \\ \Rightarrow x^2-25=0 \\ \Rightarrow \left(x-5\right)\left(x+5\right)=0 \\ \Rightarrow x=\pm 5 \\ \Rightarrow f^{-1}\left(25\right)=\left\{-5,5\right\}[\text{from}\left(1\right)\text{]} \end{gathered}$$