# What is the domain and range of f(x)=sqrtx /( x-10)?

Domain: $\left[0 , 10\right) \cup \left(10 , \infty\right)$ , Range: $\left[- \infty , \infty\right]$
$f \left(x\right) = \frac{\sqrt{x}}{x - 10}$ . Domain: under root should be $\ge 0 \therefore x \ge 0$ and denominator should not be zero, i.e $x - 10 \ne 0 \therefore x \ne 10$
So domain is $\left[0 , 10\right) \cup \left(10 , \infty\right)$
Range: $f \left(x\right)$ is any real value, i.e $f \left(x\right) \in \mathbb{R}$ or $\left[- \infty , \infty\right]$