[.] is Greatest Integer Function... Modulus is there ...
$\displaystyle \log_{[x + 1/2]} |x^2-x-2|.$
Answer is [3/2, 2) U (2, infinity)
I got the answer only (2, infinity)...
the base of $\displaystyle \log$ is always $\displaystyle > 1$. so $\displaystyle x + 1/2 \geq 2,$ which gives you $\displaystyle x \geq 3/2.$ we also need to have $\displaystyle x^2-x-2 \neq 0,$ and that gives you $\displaystyle x \neq 2.$