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