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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, if f and g be continuous functions, then
(a) `f+g` is continuous , (b) `f-g` is continuous
(c ) `fg` is continuous , (d) `(f)/(g)` is continuous at these points, where ` g(x) ne 0`.
Here, ` (g(x))/(f(x)) = ((x^(2))/(2)+1)/(2x)=(x^(2)+2)/(4x)`
Which is discontinuous at `x = 0`.
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