Question

F(x) = (a-2)x+b+3
f(-1) =2 f(3) = -4
a.b=? I need it with the explanation please :) ​

Answer 1

a = 1/2, b = -5/2.

a.b = -5/4.

Explanation:

We find f(-1) by substituting -1 for x in f(x):

f(1) = (a - 2)*-1 + b + 3

= -a + 2 + b + 3

= -a + b + 5.

So -a + b +5 = 2

-a + b = -3.

Similarly:

f(3) = (a - 2)*3 + b + 3

= 3a - 6 + b + 3

= 3a + b - 3

3a + b - 3 = -4

3a + b = -1. Also from above we have:

-a + b = -3. Subtracting:

4a = 2

a = 1/2

and b = -3 + 1/2 = - 5/2.

a.b = 1/2 * -5/2 = -5/4.

Answer 2

a = 1/2 and b = - 5/2

Explanation:

F(x) = (a-2)x+b+3

f(-1) =2 means : (a-2)(-1)+b+3 = 2

-a+2 +b+3 =2

-a+b = -3 ......(1)

f(3) = -4 means : (a-2)(3)+b+3 = -4

3a-6+b+3 =-4

3a+b =-1 ....(2)

the system is : -a+b = -3 ......(1)

3a+b =-1 ....(2)

by(1) : b = a - 3

by (2) : b = -3a -1

so : -3a-1 = a -3

-4a = -2

a = 1/2

b = 1/2 -3

b = - 5/2

anathor solution let : a-2 =m m the slope of this line

m = (-4-2)/(3-(-1)) = -6/4 = -3/2

a-2 = -3/2

so : a = 2-3/2 .... a = 1/2

f(x) =-3/2 x +b+3

f(-1) =2

(-3/2)(-1)+b+3 = 2

b = -3-3/2+2

b = -5/2