# How do you find the domain and range of f(x) = 2 / sqrt(3x-2)?

Dec 15, 2017

The domain is $\left\{x : x \in R \mathmr{and} x > \frac{2}{3}\right\}$ and the range is $\left\{y : y \in R \mathmr{and} y > 0\right\}$

#### Explanation:

The domain is the set of values which can be passed into a function. In this case, we have the constraint:

$3 x - 2 \ge 0$ (since you can't have a root of a negative number)

$3 x > 2$
$x > \frac{2}{3}$

Hence, the domain is $\left\{x : x \in R \mathmr{and} x > \frac{2}{3}\right\}$

The range is the set of values which the function can produce. As $x$ increases, the value of the root gets larger and $f \left(x\right)$ tends towards $0$. Hence the range is $\left\{y : y \in R \mathmr{and} y > 0\right\}$