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)

We have, $f^{-1}(A)=\{x ∈R:f(x)∈A\}$ Now, $f(x)∈A$ $⇒0<f(x) < 1$ $⇒ 0 < |x| < 1 ⇒-1<x < 1⇒ x∈(-1,1)$ $∴ f^{-1}(A)=(-1, 1)$.