Question

In real number system, find the domain of the function $f\left(x\right)=\frac{\sqrt{x-3}}{x-3}$.

• A. $x\ge 3$
• B. $x>3$
• C. $x<-3$
• D. $x>-3$
• E. $x<-3$ or $x>3$

Answer 1

The correct option is B $x>3$

The domain of a function $f\left(x\right)$ is the set of all values for which the function is defined.

A rational function is a function of the form $f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}$, where $p\left(x\right)$ and $q\left(x\right)$ are polynomials and $q\left(x\right)\ne 0$.

The domain of a rational function consists of all the real numbers $x$ except those for which the denominator is $0$.

To find these $x$ values to be excluded from the domain of a rational function, equate the denominator to zero and solve for $x$.

To find the excluded value in the domain of the function $f\left(x\right)=\frac{\sqrt{x-3}}{x-3}$, equate the denominator to zero and solve for $x$.

$x-3=0\Rightarrow x=3$

So, the domain of the function is $x>3$.