Choose any two specific functions (not already chosen by a classmate) that have inverses. use your chosen functions to answer any one of the following questions:
if the inverses of two functions are both functions, will the inverse of the sum or difference of the original functions also be a function?

let's took f and g, injectives, with inverses F and G.

the condition for a function to have an inverse, is that the function must be injective, it means that if f(x1) = f(x2), then x1 = x2

So f and g are injective, then f+ g is injective.

we need to see that if (f+ g)(x1) = (f + g)(x2) then x1 = x2

Now think on a counterexample for this.

if f(x) = 2x, and g(x) = -2x (both of them are injective)

then f(x) + g(x) = 0, so its not injective, so the inverse is not a function.

but f(x) - g(x) = 4x, which is injective and his inverse is a function.

Then the statement is false, because the fact that the inverses of f and g are functions, doesn't imply that the inverse of their sum or difference is also a function.

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.

because they could drop even lower..