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If f(x) = x-1x+1, then show that f(-1x)=-1f(x) - Mathematics

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Question

If f(x) = x-1x+1, then show that f(-1x)=-1f(x)

Sum

Solution

f(x) = x-1x+1

Substituting x by 1x, we get

f(-1x)=(-1x)-1(-1x)+1

= -1-xx-1+xx

= -1-x-1+x

= -(x+1)x-1

= -1x-1x+1

Therefore,

f(-1x)=-1f(x)

Hence proved.

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Chapter 2: Relations and Functions - Exercise [Page 30]

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NCERT Exemplar Mathematics [English] Class 11
Chapter 2 Relations and Functions
Exercise | Q 20.(ii) | Page 30

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