COMEDK2023MathematicsContinuity and Differentiability

If f(x)= array cl 2 x & ;- x - 2 a x+b & ;- 2 < x < 2 and it is x & ; 2 x array . continuous on [- , ] , then

Options

Aa=1 and b=1
Ba=-1 and b=-1
Ca=-1 and b=1
Da=1 and b=-1

Correct answer

D. a=1 and b=-1

Step-by-step solution

aligned & At, x= 2 & LHL = _ x / 2⁻ (a x+b)=a+b & RHL = _ x / 2⁺ ( x)=0 aligned Since, f(x) is continuous at x= / 2 aligned & At, x=- 2 & LHL = _ x - / 2⁻ (2 x)=-2 & RHL = _ x - / 2⁺ (a x+b)=-a+b aligned Since, f(x) is continuous at x=- / 2 On solving Eqs. (i) and (ii), we get a=1 and h=-1

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