Question

If domain of $f(x)=\sqrt{\frac{(x-1)(7-x)(x-5{)}^4}{x(x-5{)}^2}}$ is $D$, then number of positive integers in $D$ is

• A. 5
• B. 6
• C. 7
• D. 8

Answer 1

Answer: (B)

$\frac{(x-1)(7-x)(x-5{)}^4}{x(x-5{)}^2}\ge 0$
$\frac{(x-1)(7-x)}{x}\ge 0,x\ne 5$
$\Rightarrow x\in (-\infty ,0)\cup [1,7]-\{5\}=D$
$\Rightarrow \text{ Number of positive integers in }D=6$