JEE PYQ: Functions Question 28
Question 28 - 2019 (10 Apr Shift 1)
Let $f(x) = x^2$, $x \in \mathbb{R}$. For any $A \subseteq \mathbb{R}$, define $g(A) = {x \in \mathbb{R} : f(x) \in A}$. If $S = [0, 4]$, then which one of the following statements is not true?
(1) $g(f(S)) \neq S$
(2) $f(g(S)) = S$
(3) $g(f(S)) = g(S)$
(d) $f(g(S)) \neq f(S)$
Type: MCQ
Show Answer
Answer: (3) $g(f(S)) = g(S)$ is incorrect
Solution
$g(S) = [-2, 2]$, $f(S) = [0, 16]$, $g(f(S)) = [-4, 4]$
$g(f(S)) \neq g(S)$, so statement (3) is not true.
BETA
