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# help

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(a) Let $$f : (-\infty,0) \cup (0,\infty) \to \mathbb{R}$$ be defined by $$f(x) = x - \frac{1}{x}.$$ Show that f has no inverse function.

(b) Let $$g : (0,\infty) \to \mathbb{R}$$ be defined by $$g(x) = x - \frac{1}{x}$$ Show that g has an inverse function.

I know somebody already posted this. But how would you figure it out without plotting the graph of the function and instead do the work algebraically.

Dec 30, 2021