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Let f(x)=ax+b/cx+d.Then fof(X) =x for all x = R,provided that, a)d= -a b)d=a c)a=b=c=d=1 d)a=b=1  
Asked by g_archanasharma | 08 Apr, 2019, 05:29: AM
answered-by-expert Expert Answer
G i v e n colon space f left parenthesis x right parenthesis equals fraction numerator a x plus b over denominator c x plus d end fraction N o w space c o n s i d e r comma f left parenthesis f left parenthesis x right parenthesis right parenthesis equals x rightwards double arrow f open parentheses fraction numerator a x plus b over denominator c x plus d end fraction close parentheses equals x rightwards double arrow fraction numerator a open parentheses fraction numerator a x plus b over denominator c x plus d end fraction close parentheses plus b over denominator c open parentheses fraction numerator a x plus b over denominator c x plus d end fraction close parentheses plus d end fraction equals x rightwards double arrow fraction numerator begin display style fraction numerator a squared x plus a b over denominator c x plus d end fraction end style plus b over denominator begin display style fraction numerator a c x plus b c over denominator c x plus d end fraction end style plus d end fraction equals x rightwards double arrow fraction numerator begin display style fraction numerator a squared x plus a b plus b c x plus b d over denominator c x plus d end fraction end style over denominator begin display style fraction numerator a c x plus b c plus c d x plus d squared over denominator c x plus d end fraction end style end fraction equals x rightwards double arrow fraction numerator begin display style a squared x plus a b plus b c x plus b d end style over denominator begin display style a c x plus b c plus c d x plus d squared end style end fraction equals x rightwards double arrow a squared x plus a b plus b c x plus b d equals a c x squared plus b c x plus c d x squared plus d squared x rightwards double arrow a squared x plus a b plus b d equals a c x squared plus c d x squared plus d squared x rightwards double arrow a squared x minus a c x squared minus c d x squared minus d squared x plus a b plus b d equals 0 rightwards double arrow left parenthesis a squared minus d squared right parenthesis x minus c x squared left parenthesis a plus d right parenthesis plus b left parenthesis a plus d right parenthesis equals 0 rightwards double arrow left parenthesis a minus d right parenthesis left parenthesis a plus d right parenthesis x minus c x squared left parenthesis a plus d right parenthesis plus b left parenthesis a plus d right parenthesis equals 0 rightwards double arrow left parenthesis a plus d right parenthesis left square bracket left parenthesis a minus d right parenthesis x minus c x squared plus b right square bracket equals 0 rightwards double arrow left parenthesis a minus d right parenthesis x minus c x squared plus b equals 0 space o r space a plus d equals 0 H e n c e comma space d equals negative a
Answered by Renu Varma | 08 Apr, 2019, 10:54: AM

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