pre calculus

posted by Michelle

Find the inverse of the function below. Graph the function below and the inverse. Determine the domain, range and asymptotes of the function below and the inverse function. Please show all your work.
f(x) = 2e^-x + 5
Just looking at this gives me a headache. HELP!

1. Damon

x = 2 e^-y + 5

2 e^-y = x-5

e^-y = (x-5)/2

ln e^-y= -y = ln [(x-5)/2]

y = - ln [(x-5)/2]
= - [ ln(x-5) - ln 2 ]
y = ln 2 - ln(x-5)

2. Reiny

y = 2e^-x + 5

to form the inverse, interchange the x and y variables, so the inverse is
x = 2e^-y + 5

the inverse graph will be a reflection of the original graph in the line y = x

Pick a few ordered pairs of the original function, e.g.
(0,7), (1, 5.7) , (3, 5.1) , (-1, 10.4 ) , (-5, large) , (5, just a bit over 5)
sketch the first graph
for the inverse, switch the x and y of the ordered pairs, (same as refection in line y = x)

if you want to express your inverse as a function....
x-5 = 2e^-x
take ln of both sides
ln (x-5) = ln2 + ln e^-y
ln(x-5) - ln2 = -ylne , but lne = 1
y = ln2 - ln(x-5)
or
y = ln(2/(x-5) )

Similar Questions

1. algebra

1 (a) A function passes through the points (0, -5), (1, 0), (2, 7). Use finite differences to determine the equation of the function. (b) Draw the graph of the function. (c) Draw the inverse on the graph. (d) Show at least two different …
2. Math 3

Find the inverse of the function f(x) = 5 – e^(x-1). Determine the domain, range, and asymptotes of the function and its inverse function. Please show all of your work.
3. precalculus

Find the inverse of the function below. Graph the function below and the inverse function. Determine the domain, range, and asymptotes of the function below and the inverse function. Please show all of your work. and graph. f(x)=e^-x/2+4
4. precalculus

find the inverse of the function, graph the inverse function, determine the domain, range and asympotoes f(x)= e^-x/(2)+4
5. College Algebra

Find the inverse of the function below. Graph the function below and the inverse function. Determine the domain, range, and asymptotes of the function below and the inverse function. Please show all of your work. Show both graphs. …
6. pre calculus

The graph of a one-to-one function is shown below. Draw the graph of the inverse function, f^(-1) , and submit it to the Dropbox. Please show your work
7. pre calculus

Find the inverse of the following function. Find the domain, range, and asymptotes of each function. Graph both functions on the same coordinate plane. F(x)= ln(8-x) I am totally lost, somebody please help?