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