Question

Consider the inverse cosine​ function, defined by

y equals cosine Superscript negative 1 Baseline xy=cos−1x

or

y equals arccosine xy=arccosx.

Complete parts​ (a) through​ (d).

​(a) What is its​ domain?

nothing

​(Type your answer in interval notation. Simplify your answer. Type an exact​ answer, using

piπ

as needed. Use integers or fractions for any numbers in the​ expression.)

​(b) What is its​ range?

nothing

​(Type your answer in interval notation. Simplify your answer. Type an exact​ answer, using

piπ

as needed. Use integers or fractions for any numbers in the​ expression.)

​(c) Is this function increasing or​ decreasing?

decreasing

increasing

​(d)

arccosine left parenthesis negative one half right parenthesisarccos−12equals=StartFraction 2 pi Over 3 EndFraction2π3.

Why is

arccosine left parenthesis negative one half right parenthesisarccos−12

not equal to

negative StartFraction 4 pi Over 3 EndFraction−4π3​?

A.

Because

cosine left parenthesis negative one half right parenthesiscos−12

is not equal to

negative StartFraction 4 pi Over 3 EndFraction−4π3.

B.

Because

cosine left parenthesis negative StartFraction 4 pi Over 3 EndFraction right parenthesiscos−4π3

is not equal to

negative one half−12.

C.

Because

negative StartFraction 4 pi Over 3 EndFraction−4π3

is not in the domain of

y equals arccosine xy=arccosx.

D.

Because

negative StartFraction 4 pi Over 3 EndFraction−4π3

is not in the range of

y equals arccosine xy=arccosx.

Answer 1

a.) Domain is [-1,1].

b.)Range is [0,π].

c.)Function is decreasing.

d.) Option is D. Because -4π/3 is not in the range of y=arccos(x).

I have made the graph of y=arccos(x) you can go through it , from there you can easily know why the domain , range comes this. If you have doubt regarding the solution or how I make the graph have doubt in making the graph or how I find domain range or any other you can ask in comments.

Hope it helps