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For $$x \in R - \left\{ {0,1} \right\}$$, Let f1(x) = $$1\over x$$, f2 (x) = 1 – x and f3 (x) = $$1 \over {1 - x}$$ be three given functions. If a function, J(x) satisfies (f2 o J o f1) (x) = f3 (x) then J(x) is equal to :

JEE · Math · previous-year question

  1. A.f1 (x)
  2. B.$$1 \over x$$ f3 (x)
  3. C.f2 (x)
  4. D.f3 (x)correct

Answer

D. f3 (x)

Explanation

Given, f1(x) = $${1 \over x}$$ f2(x) = 1 $$-$$ x f3(x) = $${1 \over {1 - x}}$$ (f2 $$ \cdot $$ J $$ \cdot $$ f1) (x) = f3(x) $$ \Rightarrow $$ f2 {J(f1(x))} = f3(x) $$ \Rightarrow $$ f2{J ($${1 \over x}$$)} = $${1 \over {1 - x}}$$ $$ \Rightarrow $$ 1 $$-$$ J($${1 \over x}$$) = $${1 \over {1 - x}}$$ $$ \Rightarrow $$ J($${{1 \over x}}$$) = 1 $$-$$ $${{1 \over {1 - x}}}$$ $$ \Rightarrow $$ J ($${{1 \over { x}}}$$) = $${{ - x} \over {1 - x}}$$ = $${x \over {x - 1}}$$ Put x inplace of $${1 \over x}$$ $$ \therefore $$ J(x) = $${{{1 \over x}} \over {{1 \over x} - 1}}$$ = $${1 \over {1 - x}} = {f_3}\left( x \right)$$

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