Determine An Inverse Function

[nycmathguy]

Section 1.9
Questions 33 & 34

I say the function represented by table 33 does not have an inverse function because -2 is repeated for the y-coordinate.

I say the function represented by table 34 has an inverse function because each y-coordinate is different or not repeated.

This is way of answering the questions.

A. Am I right?

B. What is the math jargon way to express the answer?

 

[MathLover1]

correct

for future references:
In plain English, finding an inverse is simply the swapping of the x and y coordinates.
f (x) = {(2,3), (4,5), (-2,6), (1,-5)} (function)
The inverse of f (x) = {(3,2), (5,4), (6,-2), (-5,1)} (function)

Let's look at another example: g (x) = {(4,1), (8,3), (-5,3), (0,1)} (function)
The inverse of g (x) = {(1,4), (3,8), (3,-5), (1,0)} (NOT a function, x's repeat)

 

[nycmathguy]

correct

for future references:
In plain English, finding an inverse is simply the swapping of the x and y coordinates.
f (x) = {(2,3), (4,5), (-2,6), (1,-5)} (function)
The inverse of f (x) = {(3,2), (5,4), (6,-2), (-5,1)} (function)

Let's look at another example: g (x) = {(4,1), (8,3), (-5,3), (0,1)} (function)
The inverse of g (x) = {(1,4), (3,8), (3,-5), (1,0)} (NOT a function, x's repeat)

You said:

Let's look at another example:
g (x) = {(4,1), (8,3), (-5,3), (0,1)} (function)

Notice that the y-coordinates repeat 1. I thought if the y-coordinate repeats, the function has no inverse. Yes?

 

[MathLover1]

g (x) is the inverse => NOT a function, x's repeat

 

[nycmathguy]

g (x) is the inverse => NOT a function, x's repeat

Interesting.