# Thread: Inverse Functions

1. ## Inverse Functions

I need help with these 3 problems. Please explain so I can know how to do them. I did try some of them

Find a formula for the inverse of the function.

26. y=e^x/1+2e^x

Find the exact value of each expression.

34. (a) ln(1/e)= -1 I don't if that's right.

36. (b) ln(ln e^e10)

Express the given quantity as a single logarithm.

ln(1+x^2) + 1/2 ln x - ln sin x = ln sq[1+x^2]/ sin x

THis is my first week of college and it's already hard. I have a quiz tomorrow.

2. Learn to use latex!

$\displaystyle \ln \frac {1}{e}=-\ln e=-1$

$\displaystyle \ln \ln e^{e^{10}}=\ln e^{10}=10$

$\displaystyle \frac {1}{2} \ln x=\ln \sqrt x$

3. 26

You want to solve for x --this gives f^-1(y)

Clear fractions

y + 2ye^x = e^x

isolate e^x

e^x (2y-1) = -y

e^x = y/(1-2y)

Take lns

x= ln[y/(1-2y)]

f^(-1) (x) = ln[x/(1-2x)]

34a ln(1/e) = ln(1) - ln(e) I'll let you explain why this is -1

36 Not clear do you mean ln(ln[e^(10e)]) ?

For the last problem use the 3 basic prop

lna + lnb =ln(ab)

ln(a)-ln(b) = ln(a/b)

ln(a^r) = rln(a)