How do you find the domain, x intercept and vertical asymptotes of #f(x)=3lnx-1#?

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Answer 1 · 2018-07-01T12:29:11

domain #x\in(0, \infty)#, x-intercept #e^{1/3}# & asymptote #x=0#

Given function: #f(x)=3\lnx-1#

Since, Logarithms #\ln x# is defined for all positive real numbers #x>0# hence the domain of the function is

#x\in (0, \infty)#

The curve #y=3ln x-1# will intersect x-axis at which #y=0#

#0=3ln x-1#

#\ln x=1/3#

#x=e^{1/3}#

The curve #y=3\lnx-1# will touch the y-axis #(x=0)# at infinity hence the asymptotes of givem curve is #x=0#