Sets, Relations & Functions Question - None

Question

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 ?

Accepted Answer

Use [x+2]=[x]+2. Let n=[x]: n²+2n-3=0 → n=1 or n=-3. Each gives an interval of solutions → infinitely many.

Trap: Equation is in n=[x], not directly in x. Once solved, convert back to interval.

Key Concept: Floor equation → [x]=n → x∈[n,n+1)

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