Prove that if f(x) is continuous at a and f(a)≠0 then 1/f(x) is continuous at a.

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Lesson Parent: 
Function Limits VI: Continuous Functions
Problem: 

Prove that if f(x) is continuous at a and f(a)≠0 then 1/f(x) is continuous at a.

Answer: 

It is true that if f(x) is continuous at a and f(a)≠0 then 1/f(x) is continuous at a.

SAMPLE SOLUTION

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Solution: 

By the definition of continuity

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Furthermore, by the assumption of the problem we know that

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Therefore, we know that

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And again by the definition of continuity, <Sign in to see all the formulas> is continuous at a.