S1 w2 hwk
invertible functions:
find the inverse of each function. if the inverse is not a function, restrict the doma
function.
7. given: f(x) = {(-13,,-,-,-, - ,6), (9,10), (14, 32)]
find:
f'(x) =
20. f(x) = {(-3,,-,-,-5), (1. - ,,,8))
8. the function g(x) is shown on the graph below. graph the inverse of g(x) on the same set of axes.
9. is the graph of the inverse of g(x) also a function?
justify your answer.

 (7) see below   (8) see below   (9)  NO    (20) see below

Step-by-step explanation:

Inverse is when you swap the x's and y's, so switch the coordinates for the inverse.

(7)

f⁻¹(x) = (5, -13), (-9, -9), (-2, -5), (-5, 1), (-4, 0), (6, 4), (10, 9), (32, 14)

This is a function because there are no duplicate x-values.

(8)

The endpoints and vertex on the given graph are (-7, 2), (-1, -2), & (1, 4)

The graph should swap the x and y-values of the coordinates above for the endpoints and vertex, which results in (2, -7), (-2, -1) & (4, 1)

To graph the inverse, draw a line from (2, -7) to (-2, -1) and another line from (-2, -1) to (4, 1).

(9)  This is not a function because it fails the vertical line test.  In other words, there are duplicate x-values. You can draw a vertical line through x = 0 (as an example) and it touches two points.

In order to make this a function, you would have to restrict the domain to: x > 2

(20)

f⁻¹(x) = (5, -3), (-9, -2), (-2, -1), (-5, 0), (-4, 1), (6, 2), (10, 3), (8, 4)

This is a function because there are no duplicate x-values.