Question

Write an equation for the inverse cosine function, and state its domain and range.

Answer 1

See expplnation below.

Explanation:

Let's assume the following original function:

`y = cos (x)`

That represent the cosine function. Is a periodic function. With period
`T = 2\pi` and amplitude 1. And the function is between these two values
`-1,1`. So them
`Max = 1 , Min = -1`

Domain:
`(-\infty , \infty)`

Range:
`[-1,1]`

The plot for this function is on the first figure attached.

If we want to find the inverse function for the cos we just apply arccos in both sides of the original equation like this:

`arccos (y) = arccos cos(x)`

The cos and the arccos are inverse operations so then we have this:

`x= arccos (y)`

For this function the domain and range are given by:

Range:
`[0, \pi]`

Domain:
`[-1,1]`

And we can see the plot on the second figure attached.