# What is the domain of h(x) = (2x^2 + 5 )/ (sqrt(x-2))?

Sep 6, 2015

Domain: $x \in \left(2 , + \infty\right)$

#### Explanation:

In order to find the domain of $h \left(x\right)$, you need to take into account the fact that the expression under the square root must be positive for real numbers.

In other words, you cannot take the square root of a negative real number and get another real number as a solution.

Moreover, the expression under the square root cannot be equal to zero, since that would make the denominator equal to zero.

So, you need to have

$x - 2 > 0 \implies x > 2$

In interval notation, the domain of the function is $x \in \left(2 , + \infty\right)$.