SOLUTION: use the given function to answer a through f f(x)=ln(2x)+5 a. domain b. graph f c. determine range and vertical asymptote d. find f^-1 e. find domain and range for f^-1 f.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: use the given function to answer a through f f(x)=ln(2x)+5 a. domain b. graph f c. determine range and vertical asymptote d. find f^-1 e. find domain and range for f^-1 f.       Log On


   

Question 608855: use the given function to answer a through f
f(x)=ln(2x)+5
a. domain
b. graph f
c. determine range and vertical asymptote
d. find f^-1
e. find domain and range for f^-1
f. graph f^-1
Answer by lwsshak3(11628) About Me  (Show Source):
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use the given function to answer a through f
f(x)=ln(2x)+5
a. domain: (0,∞)
b. graph f (see graph below)
..
c. determine range and vertical asymptote
vertical asymptote: y-axis or x=0
range: (-∞,∞)
..
d. find f^-1
interchange x and y and solve for y which is the inverse
x=ln(2y)+5
x-5=ln(2y)
convert to exponential form
e^(x-5)=2y
y=e^(x-5)/2=f^-1
..
e. find domain and range for f^-1
domain: (-∞,∞)
range (0,∞)
Horizontal asymptote: x-axis or y=0
f. graph f^-1 (see graph below)
+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+ln%282x%29%2B5%2Ce%5E%28x-5%29%2F2%29+