Question

f(x) = | sin 4x+3 | on R ?

Answer 1

Given: f(x) = \[\left| \sin 4x + 3 \right|\] 

We know that −1 \[\leq\] sin 4x \[\leq\]1.

⇒ 2 \[\leq\] sin 4x + 3 \[\leq\]4

⇒ 2 \[\leq\] \[\left| \sin 4x + 3 \right|\] \[\leq\] 4
⇒ 2 \[\leq\] f(x) \[\leq\] 4

Hence, the maximum and minimum values of f are 4 and 2, respectively.