The domain of the function f(x)=1[x]^2-3[x]-10 is : ( where [x] denotes the greatest integ…

Question

The domain of the function $f(x)=\frac{1}{\sqrt{[x{]}^{2}-3[x]-10}}$ is : ( where $[x]$ denotes the greatest integer less than or equal to $x$ )

Accepted Answer

$f(x)=\frac{1}{\sqrt{[x{]}^{2}-3[x]-10}}$

For Domain $[x{]}^{2}-3[x]-10>0$

$\begin{gathered} \Rightarrow ([x]-5)([x]+2)>0 \ \Rightarrow [x]\in (-\infty,-2)\cup (5,\infty) \ 	herefore x\in (-\infty,-2)\cup [6,\infty) \end{gathered}$

Solutions · 1