Math Domain !!!

Calculus Level 2

A function f ( x ) f (x) is defined as :- f ( x ) { = x + a , x < 0 = x , for 0 x < 1 , = b x , x 1 f(x) \begin{cases} \displaystyle = x+a ,&& x<0 \\ \displaystyle = x , & \text {for} & 0 \leq{x}<1, \\ \displaystyle = b-x ,&& x \geq{1} \end{cases} is continuous on it's domain.

Find a + b a+b


The answer is 2.

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1 solution

Tom Engelsman
Dec 17, 2019

At x = 0 x = 0 , we require x + a = x 0 + a = 0 a = 0. x + a = x \Rightarrow 0 + a = 0 \Rightarrow a = 0. At x = 1 x = 1 , we require x = b x 2 x = b 2 ( 1 ) = b b = 2. x = b - x \Rightarrow 2x = b \Rightarrow 2(1) = b \Rightarrow b = 2. Thus, a + b = 0 + 2 = 2 . a+b = 0 +2 = \boxed{2}.

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