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

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- Oct 12th 2012, 03:21 AMAkinii 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, 04:03 AMchiroRe: 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, 04:27 AMAkiniRe: 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, 03:58 PMchiroRe: 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.