SOLUTION: Determine the domain of the function f(x) = ln (4x-x^2) I've gotten the inequality of the function which is 4x-x^2>0 but I still can't figure out what the domain is

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Determine the domain of the function f(x) = ln (4x-x^2) I've gotten the inequality of the function which is 4x-x^2>0 but I still can't figure out what the domain is      Log On


   

Question 1064212: Determine the domain of the function f(x) = ln (4x-x^2)
I've gotten the inequality of the function which is 4x-x^2>0 but I still can't figure out what the domain is
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
graph 4x-x^2 and look for the part where f(x) > 0.
graph%28300%2C300%2C-5%2C5%2C-10%2C10%2C4x-x%5E2%29

4x-x^2 must be greater than 0. ln (0) does not exist, nor does ln of a negative number
Therefore, -x^2+4x=0
same as x^2-4x=0
x*(x-4)=0
x=0 (not allowed)
x=4 (not allowed)
Need to test x between 0 and 4. Try 1,2,3
for 1, ln (3)
for 2, ln (4)
for 3, ln (3)
Try 5
ln (20-25) does not work.
Domain is 0 < x < 4
graph%28300%2C300%2C-3%2C5%2C-10%2C10%2Cln%284x-x%5E2%29%29