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  • If f(x) = 2x and g(x) = x^2/2+1 then which of the following can be a discontinuous function. A. f(x) + g(x)

If f(x) = 2x and g(x) = \frac{x^2}{2}+1 then which of the following can be a discontinuous function.
A. f(x) + g(x)
B. f(x) - g(x)
C. f(x) . g(x)
D. \frac{g(x)}{f(x)}

Answers (1)

We know that if two functions f(x) and g(x) are continuous then {f(x) +g(x)},{f(x)-g(x)}, {f(x).g(x)} and \left\{\left(\frac{\mathrm{f}(\mathrm{x})}{\mathrm{g}(\mathrm{x})}\right), \text { when } \mathrm{g}(\mathrm{x}) \neq 0\right\} are continuous.

Since, f(x) = 2x and g(x)=\frac{x^2}{2}+1 are polynomial functions, they are continuous everywhere.

⇒ {f(x) +g(x)},{f(x)-g(x)}, {f(x).g(x)} are continuous functions.

for, \frac{g(x)}{f(x)}=\frac{\frac{x^{2}}{2}+1}{2 x}=\frac{x^{2}+2}{4 x}

now, f(x) = 0

⇒ 4x = 0

⇒ x = 0

∴ \frac{g(x)}{f(x)} is discontinuous at x=0.

Posted by

infoexpert22

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