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

If `f(x)` is continuous at `x=0`, where `f(x)={:{(x^(2)+alpha", for " x ge 0),(2sqrt(x^(2)+1)+ beta", for " x lt 0):}` and `f(1/2)=2`, then

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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