WBJEE · Maths · Functions
Which of the following real valued functions is/are not even functions?
- A \(f(x)=x^{3} \sin x\)
- B \(f(x)=x^{2} \cos x\)
- C \(f(x)=e^{x} x^{3} \sin x\)
- D \(f(x)=x-[x]\), where \([x]\) denotes the greatest integer less than or equal to \(x\)
Answer & Solution
Correct Answer
(D) \(f(x)=x-[x]\), where \([x]\) denotes the greatest integer less than or equal to \(x\)
Step-by-step Solution
Detailed explanation
We know that, if \(f(-x)=f(x)\), then function is even and \(f(-x)=-f(x)\), then function is odd. (a) \(f(x)=x^{3} \sin x\) \[ \begin{aligned} f(-x) &=(-x)^{3} \sin (-x) \\ &=-x^{3}(-\sin x) \\ &=x^{3} \sin x=f(x) \end{aligned} \] So, \(f(x)\) is even. (b) \(f(x)=x^{2} \cos x\)…
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