# i really need this answer asap

• Oct 12th 2012, 04:21 AM
Akini
i really need this answer asap
Find the inverse of the following
a) f: {0,1,2,3,4) mapped to {0,1,2,3,4} defined by
f(0)=0, f(1)=3, f(2)=1, f(3)=4, f(4)=2

b) R is mapped to (0, infinite) defined by g(x) = ln(e^x + 1) for all x is in R
• Oct 12th 2012, 05:03 AM
chiro
Re: i really need this answer asap
Hey Akini.

For this problem, we know that an inverse map satisfies f(f^(-1)(x)) = x. So as an example you know f(0) = 0 which means f^(-1)(f(0)) = f^(-1)(0) = 0. Can you use this hint to get the rest of the inverse map?
• Oct 12th 2012, 05:27 AM
Akini
Re: i really need this answer asap
idk if i replied already or not (because im new to this.lol) but thanx .. and i wish i can get 1 more example from the question just to make sure i get the hang of it .. thanx
• Oct 12th 2012, 04:58 PM
chiro
Re: i really need this answer asap
Another example is f(x) = x^2 for x >= 0. y = x^2. To get an inverse function, you switch x's and y's and solve for the new y.

So we get x = y^2 => y = +SQRT(x) so f^(-1)(x) = SQRT(x) and we double check that f^(-1)(f(x)) = SQRT(x^2) = x which is >= 0 as expected.