Find the inverse

Question

Y=1+In(-x) domain, range, and the asymptote

Answer 1

y = 1 + ln(-x)

domain = {x l -x > 0} = (-∞, 0)

range = (-∞, ∞)

vertical asymptote: the x-axis (that is, the line x = 0)

Find the inverse function:

y = 1 + ln(-x)

Switch x and y: x = 1 + ln(-y)

Solve for y: x-1 = ln(-y)

e^x-1 = -y

So, y = -e^x-1

^{Domain (-∞, ∞)}

^{Range (-∞, 0)}

^{Horizontal asymptote: the y-axis (the line y = 0)}

^