Question

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) = {(-13,5),(-9,-9).(-5,-2).(-1,-5).(0, - 4),(4,6), (9,10), (14, 32)]
Find:
f'(x) =

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

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.

Answer 1

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

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.