(1 point)
Responses
lower f left parenthesis x right parenthesis equals sine x
Image with alt text: lower f left parenthesis x right parenthesis equals sine x
lower f left parenthesis x right parenthesis equals cosine x
Image with alt text: lower f left parenthesis x right parenthesis equals cosine x
lower f left parenthesis x right parenthesis equals tangent x
Image with alt text: lower f left parenthesis x right parenthesis equals tangent x
lower f left parenthesis x right parenthesis equals cosecant x
Image with alt text: lower f left parenthesis x right parenthesis equals cosecant x
lower f left parenthesis x right parenthesis equals secant x
Image with alt text: lower f left parenthesis x right parenthesis equals secant x
lower f left parenthesis x right parenthesis equals cotangent x
1 answer
The trigonometric function that requires a domain restriction of \((0, \pi)\) to be invertible is the sine function, denoted as \( f(x) = \sin(x) \).
The sine function is not one-to-one over its entire domain because it is periodic. Restricting the domain to \((0, \pi)\) ensures that the function is both continuous and monotonic (increasing), which allows it to have an inverse.
Therefore, the correct answer is:
