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If f(x)=2x and $g(x)=\Large {\frac{x^2}{2}}\normalsize+1$,then which of the following can be a discontinuous function

\begin{array}{1 1}(A)\;f(x)+g(x) & (B)\;f(x)-g(x)\\(C)\;f(x).g(x) & (D)\;\frac{g(x)}{f(x)}\end{array}

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Toolbox:
  • A function is said to be discontinuous if the $LHL\neq RHL$
  • A function is said to be discontinuous if either the LHL or RHL does not exist.
Step 1:
$f(x)=2x$ and $g(x)=\large\frac{x^2}{2}$$+1$
When function $\large\frac{g(x)}{f(x)}$ can be discontinuous function.
$\large\frac{g(x)}{f(x)}=\frac{\Large\frac{x^2}{2}+1}{2x}$
When simplified we get,
$\qquad=\large\frac{x^2+2}{4x}$
Step 2:
When $x=0$ the function is undefined .Hence it does not exist.
The function $\large\frac{g(x)}{f(x)}$ can be discontinuous.
Hence the correct option is $D$
answered Jul 4, 2013 by sreemathi.v
 
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