Find the maximum and the minimum values of `f(x)=|sin4x+3|,\ \ x in (R)` , if any.

Explanation

We have


`f(x)=|sin 4 x+3|, x in R`


`-1 leq sin 4 x leq 1 for all x in R`
`
Rightarrow-1+3 leq sin 4 x+3 leq 1+3 for all x in R`
`
Rightarrow 2 leq sin 4 x+3 leq 4 for all x in R`
`
Rightarrow 2 leq|sin 4 x+3| leq 4 for all x in R`
`
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