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IF f(x) =x^(2) + alpha for x ge 0 ...

IF `f(x) =x^(2) + alpha ` for ` x ge 0`
` = sqrt(x^(2) +1) + beta ` for ` x lt 0`
is continuous at ` x=0 and f((1)/(2))=2,` then `alpha ^(2) + beta ^(2)` is

A

3

B

`(8)/(25)`

C

`(25)/(8)`

D

`(1)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
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