I want to show f(x) =x/(x+2) is injective. I know I need to assume a is not equal to a' but f(a)=f(a') and find contradiction. Here is my start: Assume a not equal to a'. f(a)=a/(a+2) f(a')=a'/(a'+2) Now I'm not sure where to go with this?
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Originally Posted by kathrynmath I want to show f(x) =x/(x+2) is injective. I know I need to assume a is not equal to a' but f(a)=f(a') and find contradiction. Here is my start: Assume a not equal to a'. f(a)=a/(a+2) f(a')=a'/(a'+2) Now I'm not sure where to go with this? Now assume that: and that and so: then: but multiplication is comutative so aa'=a'a, and so: a contradiction. The case where either equals can easily be shown to imply the other also equals since otherwise one side is undefined while the other is defined. CB
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