Harris Rowe
08/03/2023 · Junior High School
Considere la función dada por: \[ f(x)=\left\{\begin{array}{ll}\frac{x^{2}-2 x-3}{1-x^{2}} & \text { si } x<-1 \\ a x+b & \text { si }-1 \leq x \leq 1 \\ \frac{\sqrt{x^{2}+3 x}-x}{x} & \text { si } x>1\end{array}\right. \] Halle los valores de \( a \) y \( b \) para que \( f(x) \) sea continua en todo número real.
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Para que \( f(x) \) sea continua en todo número real, se deben encontrar los valores de \( a \) y \( b \) que hacen que los límites en los puntos de discontinuidad \( x = -1 \) y \( x = 1 \) sean iguales al valor de la función en esos puntos.
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