Which of the following is true about f(x) = cases (x-2) |x-2| ( x^2-1 x^2+1 ), & x 2…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Which of the following is true about

f(x) = \begin{cases} \frac{(x-2)}{|x-2|}\left(\frac{x^2-1}{x^2+1}\right), & x \neq 2 \\ \frac{3}{5}, & x = 2 \end{cases}

(a)

f(x)

is continuous at

x = 2

. (b)

f(x)

has removable discontinuity at

x = 2

. (c)

f(x)

has non-removable discontinuity at

x = 2

. (d) Discontinuity at

x = 2

can be removed by redefining the function at

x = 2