Question

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

Answer 1

Given  : f(x) =  $2^{3\sin{4x}+1}$

To Find :   Range

Solution:

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

3 sin (4x) + 1

-1 ≤ sin (4x) ≤ 1

⇒ - 3 ≤ 3sin (4x) ≤  3

⇒  - 3 + 1  ≤ 3sin (4x) ≤  3 + 1

⇒  - 2  ≤ 3sin (4x) ≤   4

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

2⁻² ≤  f(x) ≤   2⁴

f(x) = [2⁻²  , 2⁴]

= [1/4  , 16]

Range of  $f(x) = 2^{3\sin{4x}+1}$   is   [1/4  , 16]

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Answer 2

Step-by-step explanation:

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