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If f(x) = 2x and g(x) = (x^(2))/(2)+1 ...

If `f(x) = 2x` and `g(x) = (x^(2))/(2)+1` , then which of the following can be a discontinuous functions?

A

`f(x)+g(x)`

B

`f(x)-g(x)`

C

`f(x)*g(x)`

D

`(g(x))/(f(x))`

Text Solution

Verified by Experts

The correct Answer is:
D
We know that sum, product and difference of two polynomial and polynomial function is everywhere continuous.
Now, we check the continuity of `(g(x))/(f(x))`,
` rArr (g(x))/(f(x))=((x^(2))/(2)+1)/(2x)`
Clearly, `(g(x))/(f(x))` is not defined at x = 0
`therefore` It is discontinuous at x = 0.
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