Functions #3

Calculus Level 3

$\large \tan^{-1} \left(\sqrt{\lfloor x \rfloor + \lfloor -x \rfloor}\right) + \sqrt{2-|x|} + \dfrac{1}{x^2}$

Find the sum of all the real numbers in the range of the above function.

1 solution

A Former Brilliant Member
Dec 9, 2017

Note that $x$ must be an integer because otherwise $\lfloor x \rfloor +\lfloor -x \rfloor$ would be negative.

Moreover, $2-|x| \ge 0$

$\implies -2 \le x \le 2$

Also , $x \neq 0$

So, the possible values of $x$ are $-2,-1,1,2$

Hence , the corresponding range of the function is ${2,\dfrac{1}{4}}$

So, the required answer is $2+\dfrac{1}{4}=\dfrac{9}{4}$