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As i have solved at x--> 0^{— }f(x),

there is a negative value in root which means its would be an imaginary value and hence it is discontinuous and non differentiable at x=0.

But the answer given is different.

Please explain

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If you put 0 in that expression, as x tends to 0, you will get 0. So, it is continuos at 0.

You can evaluate this limit by putting zero in this expression directly, because at x tends to 0 it is not an indeterminate form. You can also rationalize this expression first, and then evaluate the expression at x tends to 0.

I would say check your calculation. On putting 0, you don't get an imaginary value. 0 is clearly in the domain of this function.