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

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