Let $[x]$ represents the greatest integer not more than $x$. The discontinuous points of the function…
Let $[x]$ represents the greatest integer not more than $x$. The discontinuous points of the function $f(x)=\frac{5+[x]}{\sqrt{11+[x]-6 \sqrt{2+[x]}}}$ lies in the interval
$[0, \infty)$
$[5,8]$
$[7,8)$
$[7,10)$
Solution
Given the function,
$f(x)=\frac{5+[x]}{\sqrt{11+[x]-6 \sqrt{2+[x]}}}$
for discontinuous points, if $x>0$
$\begin{aligned}
& 11+[x]-6 \sqrt{2+[x]}=0 \Rightarrow(11+[x])^2=36(2+[x]) \\
& \Rightarrow[x]^2-14[x]+49=0 \Rightarrow([x]-7)^2=0 \\
& \Rightarrow[x]=7 \Rightarrow x \in[7,8)
\end{aligned}$