Problem 421 (difficulty: 2/10)

Determine the points of discontinuity of the following functions. What type of discontinuities are these?

 (1)  \(\displaystyle f(x)=\frac{x^{3}-1}{x-1},\)      (2)  \(\displaystyle g(x)=\frac{x^{2}-1}{|x-1|},\)      (3)  \(\displaystyle h_{1}(x)=x[\frac{1}{x}],\)      (4)  \(\displaystyle h_{2}(x)=x^{2}[\frac{1}{x}].\)

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