# Thread: Inverse functions with ln and log

1. ## Inverse functions with ln and log

1. I could use some guidance with a question that says "Find f^-1(3)"

Given: F(x)= 3 + x^2 + tan(PIx/2), where -1 < x < 1

I know I should find the inverse first then plug in 3 and solve. I just cannot get the inverse...

First swap x and y, but after that I cannot think of how to isolate y. I have...
x = 3 + y^2 + tan(PIy/2)

Same problem thing with

2. y = 3 + x + e^x find g^-1(4)
what is "e" just a normal variable? The book says the answer is zero...

Thanks a bunch!

Tjvelcro

2. Originally Posted by Tjvelcro
I could use some guidance with that says "Find f^-1(3)"

Given: F(x)= 3 + x^2 + tan(PIx/2), where -1 > x > 1

I know I should find the inverse first then plug in 3 and solve. I just cannot get the inverse...

First swap x and y, but after that I cannot think of how to isolate y. I have...
x = 3 + y^2 + tan(PIy/2)

Same problem thing with

y = 3 + x + e^x

what is "e" just a normal variable? The book says the answer is zero...

Thanks a bunch!

Tjvelcro
I assume you meant -1 < x < 1, since clearly we can't have -1 > 1.

Maybe this isn't the answer you're looking for, but it's not extremely hard to recognize that plugging in x = 0 results in f(0) = 3, thus $\displaystyle f^{-1}(3) = 0$. Sometimes it's easier to recognize things than to solve methodically..