Let f: R → R be a function defined by $f(x) =|x|$ for all $x ∈ R$, and let $A = (0, 1)$, then $f^{-1} (A)$ equals

(-1, 1) (0, 1) (-1, 0) none of these

(-1, 1)

The correct answer is Option (1) → (-1, 1) We have, $f^{-1}(A)=\{x∈R: f(x) ∈ A\}$ Now, $f(x) ∈ A$ $⇒0<f(x) < 1$ $⇒0 < |x| < 1⇒-1 <x < 1⇒ x∈(-1,1)$ $∴f^{-1}(A)=(-1, 1)$