MM questions

[happycat]

What I want to have clarified for me is how to find composite functions eg f(x)=rule1 and g(x)=rule2.
Under what circumstances can't a composite function exist? eg fog can but not gof. I'm also am under the impression that for an inverse of a function to exist it has to be one-one? I'm pretty sure and when can't an inverse of a function exist?

[iNerd]

From my knowledge the only part of that Q I can answer is that an inverse of a function has to be 1-1.

[vea]

If you have two functions f(x) and g(x):

Then fog=f[g(x)] and gof=g[f(x)].

For a composite function to exist, the range of the inside function must be a subset of the domain of the outside function. That basically means that the range of the inside function should be contained within the domain of the outside function.

For an inverse function to exist, the function has to be a one-to-one function---> Therefore an inverse of a function does not exist when the function is not a one-to-one function.

[xZero]

Also on the subject of composite function, if you have f(x) = something and , then f(g(x)) will always be x. Just wanted to share this rule so you won't make the same mistake as me