Find the maximum and minimum values, if any, of the following functions given by (iii) h(x) = sin(2x) + 5 (iv) f(x) = |sin 4x + 3|

(iii) Given:         ……….(i)

Since   for all  R

Adding 5 to all sides,  

Therefore, minimum value of  is 4 and maximum value is 6.

(iv) Given:  

Since   for all  R

Adding 3 to all sides,  

Therefore, minimum value of  is 2 and maximum value is 4.