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f(x) = x2 + 1. For which values of x does f(x) =
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06 Jan 2022, 10:26
1
Given that \(f(x) = x^2 + 1\) and we need to find for which values of x does \(f(x) = f (\frac{1}{x})\)
To find \(f(\frac{1}{x})\) we need to compare what is in the bracket in \(f(\frac{1}{x})\) and what is in the bracket in f(x)
=> to find the value of \(f(\frac{1}{x})\) we need to replace x with \(\frac{1}{x}\) in f(x) => \(f(\frac{1}{x})\) = \((\frac{1}{x})^2 + 1\) = \(\frac{1 + x^2 }{ x^2}\)
Now, there are two ways to solve this:
Method 1: Substitution
Take each value and find value of f(x) and f(\(\frac{1}{x}\)) and see for which value is f(x) = f(\(\frac{1}{x}\))
Re: f(x) = x2 + 1. For which values of x does f(x) =
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24 Sep 2017, 08:47
It is quite straightforward to notice that the only value of x that are equal when considered as 1/x are -1 and +1. Since in the formula for f(x) the x is squared and then summed to 1, it is easy to see that every other solution would have lead to two different values when considering x and 1/x.