# study this function : g(x) = x - 1 - ln(x)

study this function :

g(x) = x - 1 - ln(x)

## Complete answer with full step-by-step explanations

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**Problem:**

Study this function:

**Solution:**

**1st xxxxxxxxxxx**

We xxxxx the rule that the derivation of xxx xxx of xxxxxxxxx xx xxx of derivations xx functions:

Now we apply xxx rules:

and we have:

**2nd derivation:**

xx xxx get 2nd ferivation by deriving xxx xxx derivation:

xxx we apply the rules:

xxx we xxxxx

**Domain:**

xxxx of xxx function xx defined for xxxx xxxx xx xxx

However, xx xxx defined xxx each xxxx x, xxx only xxx xxxxxxxx xxxx xxxxxx of xx

xxx the xxxxxx xx the xxxxx xxxxxxxx is:

**Asymptotes:**

**vertical xxxxxxxxxxx**

xxx xxxxxxxxxx xxx xxxxxxxx xxxxxxxxxx xxx points on xxx edge of xxx interval on xxxxx the function is defined. Since our xxxxxxxx xx xxxxxxx on interval x xxx xxxx xxxxx xx which we xxxx to xxxxxx for vertical asymptote xx x and xxxx from xxx

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## here is your answer(solution with graph)

## See attachment.

The analysis is fairly simple if you remember the definition of a Lambert function (Product Log) (see http://en.wikipedia.org/wiki/Lambert_W_function ).