The function f is defined by f(x)=(x-1)(3+x), x>b-1 f(x)=-x+1, x<=b-1 and is continuous at b-1. What is b?
1 Answer
Sep 26, 2017
b=2 , orb=-3
Explanation:
We can write the function as follows:
f(x) = { (-x+1, x<=b-1), ((x-1)(3+x), x>b-1) :}
As
lim_(x rarr (b-1)^-) f(x) = lim_(x rarr (b-1)^+) f(x)
This means that:
-(b-1)+1 = ((b-1)-1)(3+(b-1))
:. -b+1+1 = (b-2)(b+2)
:. 2-b = b^2-4
:. b^2+b-6 = 0
:. (b -2)(b+ 3)= 0
Hence we have:
b=2 , orb=-3