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Asked by adjacentcalliber10 | 12 May, 2019, 15:24: PM
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f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell x squared plus a x plus 2 comma space i f space x space i s space r a t i o n a l end cell row cell 1 minus x comma space space space space space space space space space i f space x space i s space i r r a t i o n a l end cell end table close I t space i s space g i v e n space t h a t space f left parenthesis x right parenthesis space i s space d i s c o n t i n u o u s space f o r space a l l space r e a l space v a l u e s space o f space x S u p p o s e space f left parenthesis x right parenthesis space i s space c o n t i n u o u s space f o r space a l l space x rightwards double arrow x squared plus a x plus 2 equals 1 minus x rightwards double arrow x squared plus a x plus x plus 1 equals 0 rightwards double arrow x squared plus left parenthesis a plus 1 right parenthesis x plus 1 equals 0 rightwards double arrow x squared plus left parenthesis a plus 1 right parenthesis x plus fraction numerator left parenthesis a plus 1 right parenthesis squared over denominator 4 end fraction minus fraction numerator left parenthesis a plus 1 right parenthesis squared over denominator 4 end fraction plus 1 equals 0 rightwards double arrow x squared plus left parenthesis a plus 1 right parenthesis x plus fraction numerator left parenthesis a plus 1 right parenthesis squared over denominator 4 end fraction plus 1 minus fraction numerator left parenthesis a plus 1 right parenthesis squared over denominator 4 end fraction equals 0 rightwards double arrow open parentheses x plus fraction numerator a plus 1 over denominator 2 end fraction close parentheses squared plus fraction numerator 4 minus left parenthesis a plus 1 right parenthesis squared over denominator 4 end fraction equals 0 rightwards double arrow open parentheses x plus fraction numerator a plus 1 over denominator 2 end fraction close parentheses squared equals fraction numerator left parenthesis a plus 1 right parenthesis squared minus 4 over denominator 4 end fraction rightwards double arrow open parentheses x plus fraction numerator a plus 1 over denominator 2 end fraction close parentheses squared equals fraction numerator open parentheses left parenthesis a plus 1 right parenthesis minus 2 close parentheses open parentheses left parenthesis a plus 1 right parenthesis plus 2 close parentheses over denominator 4 end fraction rightwards double arrow x plus fraction numerator a plus 1 over denominator 2 end fraction equals plus-or-minus fraction numerator square root of open parentheses a minus 1 close parentheses open parentheses a plus 3 close parentheses end root over denominator 2 end fraction rightwards double arrow x equals negative fraction numerator a plus 1 over denominator 2 end fraction plus-or-minus fraction numerator square root of open parentheses a minus 1 close parentheses open parentheses a plus 3 close parentheses end root over denominator 2 end fraction S i n c e space x space i s space r e a l space rightwards double arrow open parentheses a minus 1 close parentheses open parentheses a plus 3 close parentheses greater or equal than 0 rightwards double arrow a minus 1 greater or equal than 0 space & space a plus 3 greater or equal than 0 space space O R space space a minus 1 less or equal than 0 space & space a plus 3 less or equal than 0 rightwards double arrow a greater or equal than 1 space & space a greater or equal than negative 3 space space O R space space a less or equal than 1 space & space a less or equal than negative 3 rightwards double arrow a greater or equal than 1 space space O R space space space a less or equal than negative 3 rightwards double arrow a element of left square bracket 1 comma infinity right parenthesis space O R space a element of left parenthesis negative infinity comma negative 3 right square bracket rightwards double arrow a element of left parenthesis negative infinity comma negative 3 right square bracket union left square bracket 1 comma infinity right parenthesis S i n c e space f left parenthesis x right parenthesis space i s space d i s c o n t i n u o u s comma space s o space a not an element of left parenthesis negative infinity comma negative 3 right square bracket union left square bracket 1 comma infinity right parenthesis rightwards double arrow a equals negative 2 space o r space minus 1 space o r space 0 T h u s comma space t h e space n u m b e r space o f space p o s s i b l e space i n t e g r a l space v a l u e s space o f space a space i s space 3.
Answered by Renu Varma | 15 May, 2019, 14:27: PM

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