Determine the functions f(x)=(a-1)*x-2 and g(x)=(a+1)*x+b+1 if the point of intersection of graphs of functions is (2,3).

To determine the functions f and g, we must find out the
unknown coefficients a and b.

We know that the coordinates
of the intercepting point verify the expressions of the
functions.

(2,3) belongs to f(x)'s graph if and only
if;

f(2) = 3

f(2) = (a-1)*2 -
2

Removing the brackets, we'll
get:

2a - 4 = 3 => 2a = 7 => a =
7/2

(2,3) belongs to g(x)'s graph if and only
if:

g(2) = 3

g(2)=(a+1)*2 + b
+ 1

2a + 2 + b + 1 = 3, but a =
7/2

7 + b =0  => b =
-7

The function f(x) is determined and it's expression
is:

f(x) = (7/2 - 1)*x -
2

f(x) = 5x/2 - 2

The function
g(x) is determined and it's expression is:

g(x) = (7/2 +
1)x - 7 + 1

g(x) = 9x/2 -
6

The requested functions are: f(x) = 5x/2 -
2 and g(x) = 9x/2 - 6