Question

write the maximum and minimum
values of the following
functions.sin x+4​

Answer 1

Answer:

maximum:5

minimum:3

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Answer 2

Answer:

Given,

f(x)=∣sin4x+3∣,x∈R.

we have,

−1≤sin4x≤1 for all x∈R

⇒−1+3≤sin4x+3≤1+3 for all x∈R

⇒2≤sin4x+3≤4 for all x∈R

⇒2≤∣sin4x+3∣≤4 for all x∈R

⇒2≤f(x)≤4 for all x∈R

So, the minimum and the maximum values of f(x) are 2 and 4 respectively.