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

Asked by Sakshi | 1 year ago |  71

##### Solution :-

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

Firstly, let us solve for f {f (x)}.

f {f (x)} = $$\dfrac{1}{(1 – x)}$$

= $$\dfrac{ 1 }{ 1 }– \dfrac{1}{(1 – x)}$$

= $$\dfrac{ (1 – x) }{-x}$$

$$\dfrac{ (x-1) }{x}$$

f {f (x)} = $$\dfrac{ (x-1) }{x}$$

Now, we shall solve for f [f {f (x)}]

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

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

=$$\dfrac{ 1 }{ (\dfrac{1}{x})}$$

f [f {f (x)}] = x

Hence proved.

Answered by Sakshi | 1 year ago

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