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Precalculus Mathematics Homework Help
Is f Injective? Understanding the Composition of Functions
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[QUOTE="fresh_42, post: 6045138, member: 572553"] No, it was not.They are only different if you add ##x\neq y## Yes, but that is not what you wrote. No two elements map onto the same element means: If two elements (##x, y##) happen to map to the same element (##f(x)=f(y)##), then they are equal (##x=y##): $$ f \text{ is injective } \Longleftrightarrow (f(x)=f(y) \Longrightarrow x=y) \Longleftrightarrow (x \neq y \Longrightarrow f(x)\neq f(y)) $$ However, you wrote which is the wrong direction and means that ##f## is well-defined: Different image points cannot result from one origin. I like the following mnemonic: Put your arms in front of you and let the hands be ##f##. Now make them touch at the wrist. This is not allowed for any function to be well-defined. Let them touch at the finger tips instead, then this is not allowed for injectivity. [/QUOTE]
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Precalculus Mathematics Homework Help
Is f Injective? Understanding the Composition of Functions
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