solve number 5 please

(a) (5 points) Does f attain maximum and minimum values in [-1, 1]? (b) (8 points) Is f continuous for all r e [-1, 1]? (10 points) Let f be defined for all r e (0, co) by f (@) = r+1 for TE (0, 1] 1 for r E (1, 00) Prove that f attains maximum and minimum values. Verify that nevertheless none of the conditions in the extreme-value theorem is satisfied