Mathematics - Functions Question with Solution | TestHub

If $f:[-20,20]\to R$ defined by $f(x)=\left[\frac{x^2}{a}\right]\sin x+\cos x$ is an even function , find the set of values of $\mathrm{a};[]=$.G . I. F. [0pt] [Hint: If $\mathrm{f}(\mathrm{x})$ is an even function, then $f(x)=f(-x)\Rightarrow f(x)-f(-x)=0\Rightarrow \left[\frac{x^2}{a}\right]\sin x=0$ $\Rightarrow \left[\frac{x^2}{a}\right]=a\Rightarrow 0\le \frac{x^2}{a}<1\Rightarrow a>x^2\Rightarrow a>400(\text{ since }-20\le x\le 20)\therefore a\in (400,\infty ).]$