JEE Mains · Maths · STD 12 - 1. relation and function
Let \(f(x) = x^2, x \in R\). For any \(A \subseteq R\), define \(g(A) = \{x \in R : f(x) \in A\}\). If \(S = [0, 4]\), then which one of the following statements is not true ?
- A \(f(g(S) \ne f(S)\)
- B \(f(g(S)) = S\)
- C \(g(f(S)) \ne S\)
- D \(g(f(S)) = g(S)\)
Answer & Solution
Correct Answer
(C) \(g(f(S)) \ne S\)
Step-by-step Solution
Detailed explanation
\(g\left( s \right) = \left[ { - 2,2} \right]\) \(f\left( {g\left( s \right)} \right) = \left[ {0,4} \right] = 5\) \(f\left( S \right) = \left[ {0,16} \right] \Rightarrow f\left( {g\left( s \right)} \right) \ne f\left( s \right)\)…
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