What is the inverse of the function y = 3e-^4x + 1?

Question

Answer choices

A.

B.

C.

D.

Answer 1

I'm going to assume the problem is y = 3e^-4x+1 otherwise none of the answers make sense.

To find an inverse, switch the the x's and the y's and then solve the results for "y" like this:

y = 3e^-4x+1

x = 3e^-4y+1

x/3 = e^-4y+1

ln(x/3) = ln(e^-4y+1)

ln(x/3) = (-4y+1)ln(e)

ln(x/3) = -4y + 1

ln(x/3) - 1 = -4y

(ln(x/3) - 1)/-4 = y

y = (1 - ln(x/3))/4 which is answer D

Answer 2

y = 3e^-4x + 1.

Then we interchange x and y and solve for y: x = 3e^-4y + 1; (x - 1)/3 = e^-4y, -4y = ln[(x- 1)/3]

y = -1/4ln[(x - 1)/3]

This is inverse function. It not match any of this answers.