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प्रश्न
If f(x) = `(x - 1)/(x + 1)`, then show that `f(- 1/x) = (-1)/(f(x))`
उत्तर
f(x) = `(x - 1)/(x + 1)`
Substituting x by `– 1/x`, we get
`f(- 1/x) = ((- 1/x) - 1)/((- 1/ x) + 1)`
= `((-1 - x)/x)/((-1 + x)/x)`
= `(-1 - x)/(-1 + x)`
= `(-(x + 1))/(x - 1)`
= `(-1)/((x - 1)/(x + 1))`
Therefore,
`f(- 1/x) = (-1)/(f(x))`
Hence proved.
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