Is all function a equvalence relation?

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I know that function is a type of relation. What i acctually need to know is that; Are these relations Equivalent all the times?, or it depends on the types of function?
 
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Well, what do you think yourself?? Take an arbitrary function such as f:\mathbb{R}\rightarrow \mathbb{R}x\rightarrow x^2. Does this induce an equivalence relation??
 

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