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# , or#b=-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# , or#b=-3#