Which of the following have the property that a(x)=a−1(x)? I. y=x II. y=1/x III. y=x^2 IV. y=x^3 A. I and II, only B. IV, only C. I, II, and III D. I, only

Correct

A. I and II

Step-by-step explanation:

First of all, let us have a look at the steps of finding inverse of a function.

1. Replace y with x and x with y.

2. Solve for y.

3. Replace y with

Given that:

Now, let us find inverse of each option one by one.

I. y = x, a(x) = x

Replacing y with and x with y:

x = y

x = =  Hence, I is true.

II.

Replacing y with and x with y:

=  Hence, II is true.

III.

Replacing y with and x with y:

 Hence, III is not true.

IV.

Replacing y with and x with y:

Hence, IV is not true.

Correct

A. I and II

step-by-step explanation:

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.