JEE Main 2019 — Functions Question with Solution
From: JEE Main 2019 (Online) 10th April Morning Slot
Question
Let f(x) = x2
, x R. For any A R, define g (A) = { x R : f(x) A}. If S = [0,4], then which one of the
following statements is not true ?
Choose an option
Show full solutionCorrect option: D
Correct answer
Dg(f(S)) = g(S)
Step-by-step explanation
f(x) = x2 x R
g(A) = {x R : f(x) A} S [0, 4]
g(S) = {x R : f(x) S}
= {x R : 0 x2 4}
= {x R : –2 x 2}
g(S) S
f(g(S)) f(S)
g(f(S)) = {x R : f(x) f(S)}
= {x R : x2 S2}
= {x R : 0 x2 16}
= {x R : –4 x 4}
g(f(S)) g(S)
g(f(S)) = g(S) is incorrect
g(A) = {x R : f(x) A} S [0, 4]
g(S) = {x R : f(x) S}
= {x R : 0 x2 4}
= {x R : –2 x 2}
g(S) S
f(g(S)) f(S)
g(f(S)) = {x R : f(x) f(S)}
= {x R : x2 S2}
= {x R : 0 x2 16}
= {x R : –4 x 4}
g(f(S)) g(S)
g(f(S)) = g(S) is incorrect
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