Ln equation, pls help!

1. y=ln(x+5) - 4
find formula for inverse and determine the range for the inverse.

1) First swap x and y
x=ln(y+5) - 4
2) Now to get y alone, you first add 4 to both sides
x+4=ln(y+5)
3) Then you take e^each side to cancel out the ln
e^(x+4)=(y+5)
4) Finally, subtract 5
y=e^(x+4)-5

Now, the range is simply the domain of the original equation.
To find the domain of y=ln(x+5)-4, you need to find all numbers that give you a sum of less than 0 inside the ln(x+5)
So, you make
x+5>0
x>-5
That's your domain for the original equation, so the range of the inverse would be y>-5

replace x and y and then solve for y to find the inverse
The range of the inverse is the domain of the original which is f-inverse(x) > -5
x=ln(y+5) - 4
x+4 = ln(y+5)
e^(x+4) = y+5
e^(x+4) - 5 = y

yup