Question

If the domain of the function $f\left(x\right),g\left(x\right)\in R;$ then the domain of the function $p\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}$ is equal to

• A. $R-\{x;\forall x\in f(x)=0\}$
• B. $R-\{x;\forall x\in g(x)=0\}$
• C. $R-\{x;\forall x\in f(x),g(x)=0\}$
• D. $R$

Answer 1

The correct option is B $R-\{x;\forall x\in g(x)=0\}$

Here we have given two functions $f\left(x\right),g\left(x\right)$ defined on $R.$ But $p\left(x\right)$ is a rational function so, $p\left(x\right)$ is not defined where $g\left(x\right)=0.$