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Archangel Macsika

Are the following functions from R to R? If not, explain why a) f(x) = 1/x b) f(x) = 2x + 7

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Let us check whether the following correspondings are the functions from \R  to \R.


a)    f(x) = \frac{1}{x}

Since f(x) is not defined for x=0, and for each x\ne0 the value f(x) is uniquely determined, we conclude that f is a function from \R\setminus\{0\} to \R, but f is not a function from \R to \R.


b)    f(x) = 2x + 7

Since for each x\in \R the value f(x)= 2x + 7 is uniquely determined, we conclude that f is a function from \R to \R.

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