Question

Which statement is correct about y = cos–1 x?

Answer 1

Answer:

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

Step-by-step 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.      

Answer 2

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.