Question
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.
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.
Asked by: USER9347
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440 Answers
Answer (440)
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.
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.