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

Aug 7, 2018

Domain: $x \in \left(\frac{2}{3} , + \infty\right)$
Range: $f \left(x\right) \in \mathbb{R}$

#### Explanation:

$f \left(x\right) \mathmr{and} y = \ln \left(3 x - 2\right)$

Domain: Includes all values of $x$ for which the function is defined.

$f \left(x\right)$ is undefined when $3 x - 2 \le 0$ , So, $f \left(x\right)$ is defined only

when $3 x - 2 > 0 \therefore 3 x > 2 \mathmr{and} x > \frac{2}{3}$ , Therefore,

domain , $x \in \left(\frac{2}{3} , + \infty\right)$

Range: Includes all values $y$ for which there is some $x$ such

that y=ln(3x−2). Therefore, range is any real value of $y$

i.e, $f \left(x\right) \in \mathbb{R}$.

graph{ln(3 x-2) [-10, 10, -5, 5]} [Ans]