(solution) The function F is defined by f(x)=(x-1)(3+x),x>b-1,

(solution) The function F is defined by f(x)=(x-1)(3+x),x>b-1,

The function F is defined by 

f(x)=(x-1)(3+x),x>b-1,

f(x)=-x+1,x<=b-1 .

and is continous at b-1  . What is b?

Options are :a) b=4 or b=-1 b) b=-4 or b=1 c) b=3 or b=-2 d) b=-3 or b=2
If f is continuous then
lim f x lim f x x b 1 x b 1 lim x 1 3 x lim
x b 1 x b 1 x 1 b 1 1 3 b 1 b 1 1 b 2 2 b b 2 b 2 b 2 b 2 0 b 2 b 2 1 0 b 2 b 3 0 b 2 or b 3
Thus, the correct option is d .