TS ICET 23 May 2018 Shift 1 Paper

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Question : 114 of 200

Marks: +1, -0

If |x| <1 and f(x) = 1 + x +

\x^2 + .....

then ,

\f^{-1}

(x) =

${x+1}/x$
$x/{x+1}$
${x-1}/x$
$x/{x-1}$

Solution:

Given

|x| < 1, 1 + x +x^2+x^3+...=1/{1-x}

⇒f(x)=1/{1-x}=y

(say)

⇒1-x=1/y⇒x=1-1/y={y-1}/y

Hence

f^{-1}(x)={x-1}/x

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