# Calculate a and b f(x)=ax+b and g(x)=(1+a)x-b and (1,-2), the point of intersection of f and g lines.

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### 1 Answer

Since the given point is the intercepting point of the graphs of the given functions, it's coordinates verify the expressions of the functions.

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

f(1) = -2

f(1) = a + b

a + b = -2 (1)

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

g(1) = -2

g(1)=(1+a)-b

1 + a - b = -2

a - b = -3 (2)

We'll add (1) + (2):

a + b + a - b = -2 - 3

We'll eliminate and combine like terms:

2a = -5

**a = -5/2**

We'll substitute a in (2):

a - b = -3

-5/2 - b = -3

b = 3 - 5/2

b = 1/2

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

f(x) = -5x/2 + 1/2

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

g(x) = (1 - 5/2)x + 1/2

g(x) = -3x/2 + 1/2