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.

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#### 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`

Concept: Algebra of Continuous Functions

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