Find the inverse function for f(t) = 42e^0.25t

Question

Find the inverse function for
f(t) = 42e^0.25t

I know to find an inverse you switch the x and y's but then what? do you take the log or what. I'm confused, please help me!

 

Answer 1

The exponential function and the logarithm function are inverses

 

f(t) = 42e^.25t

 

the function is written in exponential form, change this to log form

 

         Y = 42e^.25t

 

    Y/42 = e^.25t

 

log_e (y/42) = .25t

 

  Ln (y/42) = .25t

 

this would be the inverse

 

If:  Y = b^x  ; exponential

 

Then:  log_b Y = X ; logarithmic

Answer 2

Let y = f(t)

 

Then y = 42e^0.25t

 

Switch y and t:  t = 42e^0.25y

 

Solve for y :  t/42 = e^0.25y

 

                  0.25y = ln(t/42)

 

                        y = 4ln(t/42)

 

f^-1(t) = 4ln(t/42)

 

 

Answer 3

After you switch x and y, you simply solve for y from that new form.

 

x = 42e^0.25y

 

 

Solve for y using logarithms.