Given that f(x) is a linear function with f(1) + f(3) = 12 and f(4) – f(2) = 8 Find a) F(x) b) F(-1)

Answer 1

f(1)+f(3)=12

f(4)-f(2) = 8

find f(x) a linear function

y=f(x) = mx+b

y=m+b + 3m +b = 12

4m + b +b = 12

2m +b = 6

f(4) - f(2) = 8

4m+b - (2m+b) = 8

2m = 8

m=4

b = 6-2m = 6-8 = -2

b =-2

f(x) = 4x -2

f(1)+f(3) = 4-2 +3(4) -2 = 12

f(4)-f(2) = 16-2 - (8 -2)= 14-6 = 8

f(-1) = 4(-1) -2 = -6