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Which statement is correct about y = cos–1 x?
A) If the domain of y = cos x is restricted to (0,π), y = cos-1 x is a function.
B) Regardless of whether or not the domain of y = cos x is restricted, y = cos–1 x is a function.
C) If the domain of y = cos x is restricted to (-π/2, π/2), y = cos-1 x is a function.
D) Regardless of whether or not the domain of y = cos x is restricted, y = cos–1 x is not a function.

Respuesta :

altavistard
Please take just a few seconds longer and write "inverse cosine" as either:

arccos x  or


       -1   
cos      x   or


cos ^(-1)   x



A is true, since for any given x in [0, pi], there is exactly one associated y-value.

C is false.  For one input (x) value, there is more than 1 associated y-value.

Answer:

Option A - If the domain of [tex]y=\cos x[/tex] is restricted to  [tex](0,\pi)[/tex],[tex]y=\cos^{-1}x[/tex] is a function.

Step-by-step explanation:

Given : Expression [tex]y=\cos^{-1}x[/tex]

To find : Which statement is correct about the given expression?

Solution :

The domain of the inverse cosine function is [−1,1] and the range is [0,π] .

We have given the inverse function [tex]y=\cos^{-1}x[/tex]

As the domain of [tex]y=\cos x[/tex] is restricted to [tex](0,\pi)[/tex] as after [tex]\pi[/tex] the value repeats itself and not satisfying the inverse function property.

Therefore, Option A is correct.

If the domain of [tex]y=\cos x[/tex] is restricted to  [tex](0,\pi)[/tex],[tex]y=\cos^{-1}x[/tex] is a function.      

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