I am trying to find the domain of $f(x)=\ln(3x-4)$. I cannot find out how to get the domain. but I did manage to get the vertical asymptote which is $x=4/3$.
$\endgroup$ 22 Answers
$\begingroup$So the domain of a function is the set of all $x$ for which $f(x)$ is defined. The trick here is remembering that the basic natural log function $f(x) = \ln(x)$ is only defined for $x > 0$ (it is the inverse function of $y = e^x$).
Given this, your function can only take inputs when the argument of the natural log is positive. Therefore, the domain is all $x$ such that $3x - 4 > 0$.
$\endgroup$ $\begingroup$The function $\ln(\text{something})$ is defined only and only if that $\text{something}$ is strictly positive, that is $\gt 0.$ (Why?) So here all what you have to do is to recognize that your $\text{something}$ is just the expression $3x-4$. So to know where the function we're discussing is defined, solve the inequality $3x-4\gt0$.
$\endgroup$
