Question

what is the range of the function f (x) = 2 3 sin 4 x+1

Answer 1

step-by-step explanation: 3 sin (4x) + 1

-1 ≤ sin (4x) ≤ 1

⇒ - 3 ≤ 3sin (4x) ≤  3

⇒  - 3 + 1  ≤ 3sin (4x) ≤  3 + 1

⇒  - 2  ≤ 3sin (4x) ≤   4

2⁻² ≤  f(x) ≤   2⁴

f(x) = [2⁻²  , 2⁴]

= [1/4  , 16]

Range of     is   [1/4  , 16]

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