First slide

Continuity

Question

If $f (x) = sgn (x^{2} - ax + 1)$ has maximum number of points of discontinuity then

Moderate

A

$a \in (2, \infty)$
B

$a \in (- \infty, - 2)$
C

$a \in (- 2, 2)$
D

none of these

Solution

For maximum points of discontinuity of
$f (x) = sgn (x^{2} - ax + 1)$
$x^{2} - ax + 1 = 0$ must have two distinct roots, for which
$D = a^{2} - 4 > 0$
or $a \in (- \infty, - 2) \cup (2, \infty)$

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