question_answer 1)

Find the maximum and minimum values, if any of the following functions given by : (I)     f(x) = |x + 2| ? 1 (II)    g(x) = ? |x + 1| + 3 (III)   h(x) = sin (2x) + 5 (IV)  f(x) = |sin 4x + 3| (V)   h(x) = x + 1,  

Answer:

(I) f(x) = |x + 2| ? 1              f(x) = ?1 and       Max. f(x) does not exist.       (II)   g(x) = ?|x + 1| + 3             = 3 ? |x + 1|       Max. g(x) = 3 and       Min. g(x) does not exist. III.   h(x) = sin (2x) + 5       Since ?1             Min . f(x) = 6       Max. h (x = 6 IV.  f(x) = |sin (4x) + 3|       Since ? 1                          f(x) = 2 sin Max. f(x) = 4 V.   h(x) = x + 1,       Since ? 1 < x < 1        0 < x + 1 < 2        0 < h (x) < 2                                    Therefore for h(2), min. and max. values of do not exist.