Inverse function help!!?

Question

I have to find the inverse function of:

f(t) = 1 + ln t

I just need help on how to find it primarily. Individual step by step instructions would do wonders!! Thanks :)

Answer 1

f(t) = 1 + ln t

y = 1 + ln t

Swap positions of y and t

t = 1 + ln y

Solve for the new y

t - 1 = ln y

y = e^(t-1)

The new y is the inverse function of the original.

f inverse(t) = e^(t-1)

Answer 2

So let's pretend f(t) = y and t = x. That would give us y = 1 + ln x.

The first step to finding the inverse of any function is the switch the places of the x and y. In this case, you'd get x = 1 + ln y. Then, it's as simple as solving for y for the new equation.

x = 1 + ln y

x - 1 = ln y

e^(x - 1) = y

ANSWER: f^-(t) = e^(t - 1)