Let f(x)=(1−x)2sin2x+x2 for all x∈R. Consider the statements:P: Th – InterviewSolution

1.	Let f(x)=(1−x)2sin2x+x2 for all x∈R. Consider the statements:P: There exists some x∈R such that f(x)+2x=2(1+x2).Q:There exists some x∈R such that 2f(x)+1=2x(1+x).Then
Answer» Let $f (x) = (1 - x)^{2} s i n^{2} x + x^{2}$ for all $x \in R$ . Consider the statements: P: There exists some $x \in R$ such that $f (x) + 2 x = 2 (1 + x^{2}) .$ Q:There exists some $x \in R$ such that $2 f (x) + 1 = 2 x (1 + x) .$ Then

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