# 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).

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The functions given are : f(x)=(a-1)*x-2 and g(x)=(a+1)*x+b+1. The point of intersection of the two is (2 , 3)

Equating (a-1)*2 - 2 = (a+1)*2+b+1

=> 2a - 2 - 2 = 2a + 2 + b + 1

=> b = -7

3 = (a + 1)*2 - 7 + 1

=> 3 = 2a + 2 - 6

=> 2a = 7

=> a = 7/2

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

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**