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If f is continuous at x=0 , where f(x)=x...

If `f` is continuous at `x=0` , where `f(x)=x^2+alpha` ,`x>=0`, `f(x)=2sqrt(x^2+1)+beta`, `x<0`. Find `alpha` and `beta` given that `f(1/2)=2`

A

`alpha=(-1)/(4), beta=7/4`

B

`alpha=(-7)/(4), beta=1/4`

C

`alpha=1/4, beta=(-7)/(4)`

D

`alpha=7/4, beta=(-1)/(4)`

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The correct Answer is:
D
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