- #1
John O' Meara
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Homework Statement
Prove: if f and g are one-to-one (i.e., invertible), then so is the composition [tex] f \circ g[/tex]
Homework Equations
I think you prove that the composition f o g has an inverse? As, a function has an inverse if and only if it is one-to-one.
The Attempt at a Solution
[tex](f \circ g)^{-1}((f \circ g)(x))=x\\ (f \circ g)((f \circ g)^{-1}(x))=x. \\ (f \circ g)^{-1}((f \circ g)(x))= (f(g(x)))^{-1}(f(g(x))) = f^{-1}(g(x)^{-1})(f(g(x)))[/tex]. I wonder can I do just what I have just done? Help gratefully received, thank you.