functions and logs

[Tueseve728]

I am stuck trying to figure out the domain and range to these problems...
1) h(x)=1/(e-e^x)

2)f(x)=1/(1+e^x)

then solve the equation ln(y-1)-ln 2=x + ln x, for y in terms of x.

 

[stapel]

The domain is all allowable x-values. In these cases, the only disallowed x-values would be those that made the denominators equal to zero (since you can't divide by zero). So set the denominators equal to zero; the domains will be all other x-values.

For finding the range, what sorts of techniques have you been using in class? Are you just eyeballing the range from the graph, or are you proving things with max/min points and such?

For the log-equation problem, I don't see how you could solve this algebraically. I may just be missing something, but with that "x" outside of any log, I don't see how you're supposed to proceed. Sorry.

Eliz.

 

[jimi]

ln(y-1)-ln 2=x + ln x

ln ((y-1)/2) = x + ln x
(y-1)/2 = e^(x + ln x) = (e^x)(e^ln x) = xe^x
y-1 = 2xe^x
y = 2xe^x + 1