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Prove that if f(x) is a continuous function and f(x) is not zero then g(x) =...

Prove that if f(x) is a continuous function and f(x) is not zero then g(x) = 1/f(x) is a continuous function.  

Use the epsilon-delta definition of continuity and please overexplain and check your work before answering.

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I did this example with enough explanation I hope. If you found any difficulty please let me know in comments. I'll make it clear for you. Thank you

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