(1) If $f$ is a continuous function and $\lim _{x \rightarrow 1}(3+f(x))=2$, then $f(1)=$
(2) If $g(x)=\left\{\begin{array}{ll}x^{2}, & x< 1 \\ a x+3, & x \geq 1\end{array}\right.$ is a continuous function, then $a=$
(3) The discontinuity point(s) of the function $f(x)=\frac{x}{x^{2}-2 x-3}$ is (are)

Answer

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Answer

The discontinuity points of the function f(x) are $\boxed{-1}$ and $\boxed{3}$

Steps

Step 1 ：Find the value of f(1) given that $\lim_{x \rightarrow 1}(3+f(x))=2$

Step 2 ：Find the value of a such that $g(x) = \left\{\begin{array}{ll}x^{2}, & x<1 \\ a x+3, & x \geq 1\end{array}\right.$ is continuous

Step 3 ：Find the discontinuity points of the function $f(x) = \frac{x}{x^{2} - 2x - 3}$

Step 4 ：f(1) = \boxed{-1}

Step 5 ：a = \boxed{-2}

Step 6 ：The discontinuity points of the function f(x) are $\boxed{-1}$ and $\boxed{3}$