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  • The function f(x) = 4-x^2/4x-x^3 is A. discontinuous at only one point B. discontinuous at exactly two points C. discontinuous at exactly three points D. none of these

The function f(x) = \frac{4-x^2}{4x-x^3} is
A. discontinuous at only one point
B. discontinuous at exactly two points
C. discontinuous at exactly three points
D. none of these

Answers (1)

Solution

We have, f(x) = \frac{4-x^2}{4x-x^3}

Now, f(x)  is discontinuous where 4 x-x^{3}=0
\\\Rightarrow x\left(4 x-x^{2}\right)=0 \\\Rightarrow x=0\ or\ 4 x-x^{3}=0 \\\Rightarrow x=0\ or\ x=\pm 2
\Rightarrow f(x) is discontinuous at exactly three points.

Correct option is D.

Posted by

infoexpert22

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