hi again, its functions f and g have domains (0,infinity) and (0,pi/4] respectively and are f(x) = lnx and g(x)=tanx.
write the domain and range of fg(x) (for which i got D(0,pi/4] and R(-infinity,0])
solve fg(x)=-0.4 (for which i got 33.84)
and give a value of k so that when fg(x)=k has no solution, with a reason.
I have demonstrated the periodicity of the tangent function, explained how this affects the domain of the composite function given the restriction placed on the tangent function by the natural logarithm function, and stated what the range of the composite function is.
If you are to give a coherent explanation of all of this, it should be in your words. This is a good part of doing mathematics, being able to explain your findings in a lucid and logical manner. Often, increased understand comes from doing this. As a student, I used to keep a math journal, where I tried to record my explorations in as clear a manner as I could and I found I gained a better depth of understand just by doing this.
I will help you with this by offering suggestions to your writing, but I would be robbing you of a good opportunity here to learn if I write a summary for you. This topic has all the information you need, so review it and see if you can summarize what we have found.