What is the domain and range of $f (x) = ln (x) : x > 0$ $f(x) = ln(x): x>0$ ?

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Answer 1 · 2016-09-26T01:05:15

$(- \infty, + \infty)$ $(-oo,+oo)$

$f (x) = ln x$ $f(x) = lnx$ is, as you state, defined for $x > 0$ $x>0$ . Thus its domain is $0, + \infty)$ $0,+oo)$ .

On the other hand, since $lim_"x->0"lnx =-oo$ the range of $lnx$ is $(-oo,+oo)$

We can get a sense of this by looking at the graph of $lnx$ below:

graph{lnx [-1.596, 9.504, -3.33, 2.217]}

What is the domain and range of f(x) = ln(x): x>0f(x)=ln(x):x>0f(x) = ln(x): x>0?