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Question
Which one of the following functions has the property f(x) = `"f"(1/x)`?
Options
f(x) = `(x^2 - 1)/x`
f(x) = `(1 - x^2)/x`
f(x) = x
f(x) = `(x^2 + 1)/x`
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Solution
f(x) = `(x^2 + 1)/x`
Explanation:
f(x) = `"f"(1/x)`
take f(x) = `(x^2 + 1)/x`
`"f"(1/x) = ((1/x)^2 + 1)/(1/x) = (1/x^2 + 1)x`
`= (1 + x^2)/x^2 xx x`
`= (x^2 + 1)/x` = f(x)
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