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.

Answer 1

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 2

Option A - If the domain of
`y=\cos x` is restricted to
`(0,\pi)`,
`y=\cos^(-1)x` is a function.

Explanation:

Given : Expression
`y=\cos^(-1)x`

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
`y=\cos^(-1)x`

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

Therefore, Option A is correct.

If the domain of
`y=\cos x` is restricted to
`(0,\pi)`,
`y=\cos^(-1)x` is a function.