Answer:

Step-by-step explanation:
Pythagorean Theorem: 
In this case, a = 9, b = a, and c = 15.


The, we subtract 81 from both sides getting:
,
Then, 
In this relation we have two ordered pairs:
( 5, 7 ) and ( 5, 8 )
For x = 5 : f ( x ) = 7 and also for x = 5, f ( x ) = 8. This is not possible for a function.
Answer:
b ) No. The relation is not a function.
Answer:
3x+1.
Step-by-step explanation:
First we divide g(x)/f(x) (the process is in the first image):
5x-15 in Z7[x] is 5x-1 and
is
in Z7[x]. So
g(x)/f(x) = 
Now gcd(g,f) = gcm(f,r).
f(x)/r(x) = 
Then, gcd(f,r) = gcd(r,3x+1).
r/(3x+1) = 
Then, gcd(r, 3x+1) = gcd(3x+1,4) = 3x+1.
So, gcd(f,g) = 3x+1.
You have to make the denominators(bottom of the fraction) the same in order to combine the fractions.
To make the denominator of
the same as
, you multiply the top and bottom of the fraction by 2 (because they both have a common multiple of 4)

So:

Yes this is correct answer