16. Discuss the continuity of the function f, where f is defined by

Answers (1)

Given function is

GIven function is defined for every real number k
Different cases are their
case (i)  k < -1

Hence, given function is continuous for every value of k < -1

case(ii)    k = -1

Hence, given function is continous at x = -1

case(iii)  k > -1

Hence, given function is continous for all values of  x > -1

case(vi)   -1 < k < 1

Hence, for every value of k in -1 < k < 1 given function is continous

case(v)  k = 1

Hence.at  x =1 function is continous

case(vi)  k > 1

Hence, given function is continous for each and every value of k > 1
case(vii)  when k < 1

Hence, for every value of k in k < 1 given function is continuous

Therefore, continuous at all points

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