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Let I be any interval disjoint from `(1, 1)`. Prove that the function f given by `f(x)=x+1/x`is strictly increasing on 1.

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` f(x) = x + 1/x, x ne 0`
` rArr f'(x) = 1 - 1/x^(2) = (x^(2)-1)/x^(2) = ((x-1)(x+1))/x^(2)`
If `f'(x) = 0" then "(x-1)(x+1)=0`
` rArr x=1, -1`
Now, divide R into intervals ` (-infty, -1),(-1, 1) and (1, infty)`.

`:. f(x)" is increasing in "I=(-infty, -1) cup (1, infty)`.
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