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Question
A function f (x) is defined as
f (x) = x + a, x < 0
= x, 0 ≤x ≤ 1
= b- x, x ≥1
is continuous in its domain.
Find a + b.
Solution
f (x) is continuous in its domain.
f (x) is continuous at x = 0 & x = 1
Since f(x) is continuous at x = 0
`therefore lim_(x->0^-)f(x)=lim_(x->0^+)f(x)=f(0)`
`lim_(x->0)(x+a)=lim_(x->0)x=0`
`0+a=0`
`a=0`
Also f (x) is continuous at x = 1
`therefore lim_(x->1^-)f(x)=lim_(x->1^+)f(x)=f(1)`
`lim_(x->1)(x+a)=lim_(x->1)(b-x)=b-1`
`1=b-1`
`b=2`
`a+b=2`
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