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  • State True or False for the statements If f .g is continuous at x = a, then f and g are separately continuous at x = a.

State True or False for the statements
If f.g is continuous at x = a, then f and g are separately continuous at x = a.

 

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Solution

False

Let f(x)=x and g(x)=\frac{1}{x}
f(x) \cdot g(x)=x \cdot \frac{1}{x}=1, which is a constant function and continuous everywhere.
But, g(x)=\frac{1}{x} is discontinuous at $x=0$.

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infoexpert22

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