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Question

Find the values of a and b such that the function defined by f(x)=5,ifx2ax+b,if2<x<1021,ifx10 is a continuous function.

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Solution

f(x)=5,ifx2ax+b,if2<x<1021,ifx10

If the function f(x) is a continuous function, then
f(2)=f(2+) and f(10)=f(10)

I:f(2)=f(2+)
5=2a+b ... (i)

II:f(10)=f(10)
10a+b=21 ...(ii)

from (i) and (ii), we get
a=2,b=1

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