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What is the domain of the inverse of the function f(x) = sin (3x + 2)

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The function f(x) = sin (3x + 2). The range of f(x) is [-1, 1] as the sine of any angle is either less than or equal to 1 or greater than or equal to -1.

y = f(x) = sin (3x + 2)

3x + 2 = arc sin y

Now arc sin y can only take on values that lie in [-1, 1]

3x + 2 lies in [-1, 1]

3x lies in [-3, -1]

x lies in [-1, -1/3]

 

The domain of the inverse of f(x) = sin (3x + 2) is [ -1, -1/3]

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