Question

If $h\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}$, where $f\left(x\right)=x^2-2x$ and $g\left(x\right)=x^3-3x^2+2x,$ then the number of integers which are not present in the domain of ${\left(h\right(x\left)\right)}^{1/1001}$ is

• A. 3
• B. 3.0
• C. 3.00
• D. 03

Answer 1

Answer: (A), (B), (C), (D)

We know that, domain of $\left(p\right(x){)}^{1/\text{odd integer}}=$ domain of $p\left(x\right)$
$\therefore$ domian of ${\left(h\right(x\left)\right)}^{1/1001}=$ domain of $h\left(x\right).$
$h\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}=\frac{x^2-2x}{x^3-3x^2+2x}\Rightarrow h\left(x\right)=\frac{x(x-2)}{x(x^2-3x+2)}\Rightarrow h\left(x\right)=\frac{x(x-2)}{x(x-1)(x-2)}$
Here, $x(x-1)(x-2)\ne 0$
$\therefore$ The domain of function $h\left(x\right)$ is $R-\{0,1,2\}$