Question

What is the range of the function f(x) = 2^3 sin 4z +1 ?​

Answer 1

Given : f(x) = 2^{3\sin{4x}+1}2

3sin4x+1

To Find : Range

Solution:

f(x) = 2^{3\sin{4x}+1}f(x)=2

3sin4x+1

3 sin (4x) + 1

-1 ≤ sin (4x) ≤ 1

⇒ - 3 ≤ 3sin (4x) ≤ 3

⇒ - 3 + 1 ≤ 3sin (4x) ≤ 3 + 1

⇒ - 2 ≤ 3sin (4x) ≤ 4

f(x) = 2^{3\sin{4x}+1}f(x)=2

3sin4x+1

2⁻² ≤ f(x) ≤ 2⁴

f(x) = [2⁻² , 2⁴]

= [1/4 , 16]

Range of f(x) = 2^{3\sin{4x}+1}f(x) = 2^{3\sin{4x}+1}f(x)=2

3sin4x+1

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