Question

Consider the following relation.

y=−x−5

Find four points contained in the inverse. Express your values as an integer or simplified fraction.

{( , ), ( , ), ( , ), ( , )}

Answer 1

To sum up the concept of inverse function

If you have function f(x)

if f(\(\color{orange}{x}\)) = \(\color{red}{a}\)

then your inverse function \( f^{-1}(x)\)

would be
\( f^{-1}(\color{red}{a}) = \color{orange}{x}\)

the x-value of the inverse function is going to be the y-value of the normal function

the y-value of the inverse function is going to be the x-value of the normal function

Answer 2

so you have two ways to answer this question:

1)
you can find points that belong to the function y = -x-5
and then flip them

so (x, y) becomes (y, x)

2) you can find the inverse function and then find points that belong to it

Answer 3

If you want to go with the first method,

just plug in whichever x-values you like and solve for y
and then flip the x and y values

so for example, if you plug in x = 1, what do you get for y?

That point (x, y) is going to be the point for y = -x-5

The point that lies on the inverse function is going to be (y, x)
you just switch those two values around

Answer 4

If you'd like to go with the second method, then you have to first find the inverse function using the following steps:

first change y to x
and change the x to y

Once you do that, you have to solve the equation for the new y

After you get your inverse function, you can just plug in values for x and solve for y. Those will be the points that are contained in the inverse