If f (x) = (x + 1) / (x – 1), show that f [f (x)] = x.

If f (x) = \(\dfrac{ (x + 1) }{ (x – 1)}\), show that f [f (x)] = x.

Asked by Sakshi | 1 year ago |  77
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Class 11 Maths Relations and Functions         Add Answer

1 Answer

Solution :-

Given:

f (x) =\(\dfrac{ (x + 1) }{ (x – 1)}\)

Let us prove that f [f (x)] = x.

f [f (x)] =\( \dfrac{f (x+1)}{(x-1)}\)

=\(\dfrac{ (x+1+x-1)}{(x+1-x+1)}\)

= \( \dfrac{2x}{2}\)

= x

f [f (x)] = x

Hence proved.

Answered by Sakshi | 1 year ago
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