QJEEM19Macd6e: JEE Main 2019 Mathematics - Class 11 JEEM19Macd6e Solution: For , Let f 1 (x) = , f 2 (x) = 1 – x and f 3 (x) = be three…

Question

Verified Solution • 2025–26 Session moderate

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 :

Accepted Answer

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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