Find an explicit formula for f^(-1) and use it to graph f^(-1), f, and the line y=x on the same screen. To check your work, see whether the graphs of f and f^(-1) are reflections about the line.

f(x)=2-e^(x)

Question

Find an explicit formula for f^(-1) and use it to graph f^(-1), f, and the line y=x on the same screen. To check your work, see whether the graphs of f and f^(-1) are reflections about the line.

f(x)=2-e^(x)

jim_thompson5910 · Answer

f(x)=2-e^(x)

y=2-e^(x)

Swap x and y to get

x = 2 - e^y

Now solve for y

x-2 = -e^y

e^y = -x + 2

I'll let you finish

anonymous · Answer

can you explain what I'm supposed to do.. I don't even understand what its asking.

jim_thompson5910 · Answer

Do you know how to solve e^y = -x+2 for y?

anonymous · Answer

no lol.

jim_thompson5910 · Answer

when we want to isolate exponents, what do we use?

anonymous · Answer

no idea....

anonymous · Answer

chain rule..?

jim_thompson5910 · Answer

to undo addition, we use subtraction (or vice versa)

to undo division, we use multiplication (or vice versa)

to undo exponentiation, we use logs (or vice versa)

etc

jim_thompson5910 · Answer

so to solve 2^x = 16, we use logs

jim_thompson5910 · Answer

what do you get when you solve 

e^y = -x+2

for y? (use logs)

anonymous · Answer

do i use ln?

jim_thompson5910 · Answer

yes, ln (LN) is the natural log (it's a log with base 'e')

anonymous · Answer

ln(-x+2)?

jim_thompson5910 · Answer

so y = ln(-x + 2)

jim_thompson5910 · Answer

the last thing to do is replace y with $\Large f^{-1}(x)$ to get the inverse

$$\Large f^{-1}(x) = \ln(-x+2)$$