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