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Byju's Answer

Standard XII

Mathematics

Right Hand Limit

If fx = sgn...

Question

If $f (x) = s g n (x^{2} - a x + 1)$ has maximum number of points of discontinuity, then

a \in (1, 0)

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a \in (- 1, 1)

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a \in (- \infty, - 2) \cup (2, \infty)

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a \in (- 2, 2)

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Solution

The correct option is A $a \in (- \infty, - 2) \cup (2, \infty)$
$f (x) = s g n (x^{2} - a x + 1)$
For $f (x)$ to have maximum number of points of discontinuity.
Roots of quadratic equation $x^{2} - a x + 1 = 0$ should be real and different
$\Rightarrow D > 0 \Rightarrow a^{2} - 4 > 0 \Rightarrow a ϵ (- \infty, - 2) \cup (2, \infty)$

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