If a and b(a > b) are points of discontinuity of the function f(x)=3−2x2, for x≤02x+3, for 0<x≤12x2−3x, for 1<x<22x−3, for 2≤x<3|x| , for x≥3 then3a - b =

Ltx→0⁡f(x)=Ltx→0−3−2x2=3,Ltx→0+f(x)=Ltx→0+2x+3=3. Ltx→1-⁡f(x)=Ltx→1-2x+3=5,Ltx→1+f(x)=Ltx→1+2x2−3x=−1.Ltx→2−f(x)=Ltx→2−2x2−3x=0, Ltx→2+f(x)=Ltx→2+2x−3=1⇒a=2,b=1⇒3a−b=5.

If a and b(a > b) are points of discontinuity of the function f(x)=3−2x2, for x≤02x+3, for 0<x≤12x2−3x, for 1<x<22x−3, for 2≤x<3|x| , for x≥3 then3a - b =

Ltx→0⁡f(x)=Ltx→0−3−2x2=3,Ltx→0+f(x)=Ltx→0+2x+3=3. Ltx→1-⁡f(x)=Ltx→1-2x+3=5,Ltx→1+f(x)=Ltx→1+2x2−3x=−1.Ltx→2−f(x)=Ltx→2−2x2−3x=0, Ltx→2+f(x)=Ltx→2+2x−3=1⇒a=2,b=1⇒3a−b=5.

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If a and b(a > b) are points of discontinuity of the function $f (x) = \{\begin{cases} 3 - 2 x^{2}, for x \leq 0 \\ 2 x + 3, for 0 < x \leq 1 \\ 2 x^{2} - 3 x, for 1 < x < 2 \\ 2 x - 3, for 2 \leq x < 3 \\ | x |, for x \geq 3 \end{cases}$ then3a - b =

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Detailed Solution

$\begin{array}{l} \underset{x \to 0}{L t} f (x) = \underset{x \to 0 -}{L t} (3 - 2 x^{2}) = 3, \underset{x \to 0 +}{L t} f (x) = \underset{x \to 0 +}{L t} 2 x + 3 = 3 . \\ \underset{x \to 1 -}{L t} f (x) = \underset{x \to 1 -}{L t} 2 x + 3 = 5, \underset{x \to 1 +}{L t} f (x) = \underset{x \to 1 +}{L t} 2 x^{2} - 3 x = - 1 . \\ \underset{x \to 2 -}{L t} f (x) = \underset{x \to 2 -}{L t} 2 x^{2} - 3 x = 0, \underset{x \to 2 +}{L t} f (x) = \underset{x \to 2 +}{L t} 2 x - 3 = 1 \Rightarrow a = 2, b = 1 \Rightarrow 3 a - b = 5 . \end{array}$