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Question

Consider the function
f(x)=2x1,0x<2x+a2x43x+b4<x6
(i) Find f(2) and f(2+)
(ii) Find a if f is continuous at x=2
(iii) Find b if f is continuous on [0,6]

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Solution

f(x<2)=2x1
f(2)=2(2)1=3
f(x>2)=x+a
f(2+)=2+a
Given that f is continous at x=2
f(2)=f(2+)
2+a=3
a=1
Given that f is continous on [0,6]
f(4)=f(4+)
4+a=12+b
41=12+b
b=9

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