Let $f(x) = {x^2},x \in R.$ For any $A \subseteq R,$ define $g(A) = \left\{ {x \in R:f(x) \in A} \right\}.$ If $S = \left[ {0,4} \right],$ then which one of the following statements is not true?

JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

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Analyzing +4 | -1

Let

f(x) = {x^2},x \in R.

For any

A \subseteq R,

define

g(A) = \left\{ {x \in R:f(x) \in A} \right\}.

S = \left[ {0,4} \right],

then which one of the following statements is not true?

View answer and explanation

Correct option: C

g(f(S)) = g(S)

Option C (

g(f(S)) = g(S)

) is correct because it is NOT true. g(f(S)) = [-4, 4] and g(S) = [-2, 2], so they are not equal.