If `f(x)=f(x)={(sin(a+1)x+sinx)/(x^x c),x<0(sqrt(x+b x^2)-sqrt(x))/(b xsqrt(x)),xgeq0,` is continuous at `x=0,t h e n` `(a)a=-3/2,b=0,c=1/2` (b) `a=-3/2,b=1,c=-1/2` `a=-3/2,b in R-[0],c=1/2` (d) none of these

Explanation

To determine the conditions under which the function \( f(x) \) is continuous at \( x = 0 \), we need to analyze the left-hand limit (LHL), right-hand limit (RHL), and the function value at \( x = 0 \).

The function is defined as follows:

\[
f(x) =
\begin{cases}
\frac{\sin((a+1)x) + \sin x}{x^x c} & \text{if } x < 0 \\
...