The function `f(x)={(x^2/a, if 0le x lt1),(a, if 1 le x lt sqrt2),((2b^2-4b)/(x^2), if `sqrt(2) le xlt 00):}` is continuous on `[0,oo]dot` Find the most suitable values of `a` and `bdot`

Explanation

f is continuous at `x=1`

`implies lim _{x -> 1^-} f(x)=a`

`implies lim _{x -> 1^-} {x^2}/a=a`

`implies a=pm1`

f is continuous at `x=sqrt2`

`implies lim _{x -> sqrt2^+} f(x)=a`

`implies lim _{x -> sqrt2^+} {2b^2-4b}/x^2=a`

`implies{2b^2-4b}/2=a`

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