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Question

Let a,bR,(a0). If the function f defined as
f(x)=⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪2x2a ,0x<1a ,1x<22b24bx3 ,2x<
is continuous in the interval [0,),,then an ordered pair (a,b) is:

A
(2,13)
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B
(2,1+3)
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C
(2,13)
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D
(2,1+3)
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Solution

The correct option is A (2,13)
This function to be continuous in the interval (0,)
limx12x2a=a=limx22b24bx3
By solving the above equation
(a,b)=(2,13)

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