Choose the correct answer from given four options in each of the Exercises from 83 to 96. If f(x)=2x and g(x)=x22+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) g(x)f(x)

Choose the correct answer from given four options in each of the Exercises from 83 to 96.

If $f (x) = 2 x$ 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) $f (x) \cdot g (x)$

(D) $\frac{g (x)}{f (x)}$

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Alok Kumar Singh | Contributor-Level 10

9 months ago

This is an Objective Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} W e k n o w t h a t t h e algebraic polynomials are continuous functions everywhere. \\ ∴ f (x) + g (x) i s c o n t i n u o u s [\begin{array}{l} ? S u m, d i f f e r e n c e a n d p r o d u c t o f t w o c o n t i n u o u s \\ f u n c t i o n s i s a l s o c o n t i n u o u s \end{array}] \\ f (x) - g (x) i s c o n t i n u o u s \\ f (x) . g (x) i s c o n t i n u o u s \\ \frac{g (x)}{f (x)} i s o n l y c o n t i n u o u s i f g (x) \neq 0 \\ ∴ \frac{f (x)}{g (x)} = \frac{2 x}{\frac{x^{2}}{2} + 1} = \frac{4 x}{x^{2} + 2} \\ H e r e, \frac{g (x)}{f (x)} = \frac{\frac{x^{2}}{2} + 1}{2 x} = \frac{x^{2} + 2}{4 x} w h i c h i s d i s c o n t i n u o u s a t x = 0 . \\ H e n c e, t h e c o r r e c t o p t i o n i s (d) \end{array}$

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Kindly go through the solution