Given this function , I have to find its inverse. How do you do that, and which is its inverse?

I am clueless, and I unfortunately need this answer tomorrow. I would hugely appreciate any help with this.

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- Jun 24th 2012, 03:04 PMkkmInverting a function
Given this function , I have to find its inverse. How do you do that, and which is its inverse?

I am clueless, and I unfortunately need this answer tomorrow. I would hugely appreciate any help with this. - Jun 24th 2012, 03:19 PMPlatoRe: Inverting a function
- Jun 24th 2012, 03:23 PMkkmRe: Inverting a function
Could you please show me how to solve for ?

- Jun 24th 2012, 03:39 PMpickslidesRe: Inverting a function
Cube both sides, subtract 1, multiply by -1 then take the cube root.

- Jun 24th 2012, 03:46 PMPlatoRe: Inverting a function
- Jun 24th 2012, 10:42 PMDevenoRe: Inverting a function
another way to look at this is:

the inverse of a composition is the reverse composition of the inverses:

.

to see that this is so, recall that an inverse of a function (provided one does exist) is a function g so that f(g(x)) = g(f(x)) = x.

we can write this as: .

so let's calculate .

since no matter what "t" is, we have (taking ),

.

the proof that is entirely similar.

now let's look at "your function":

.

this is the composition of 3 functions:

, where

a little thought should convince you that:

(note that means k is g's inverse)

(h is its own inverse, this can happen)

(and as we would expect, g is k's inverse).

in short,

you might find this slightly amazing.

what this means is: .

let's "try it" with some actual number, instead of x. how about x = 5?

ok, that's kind of a weird number. so let's find f(x) when .

. huh. how about that? - Jun 25th 2012, 05:04 AMkkmRe: Inverting a function