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Asked by adjacentcalliber10 | 12 May, 2019, 15:28: PM
answered-by-expert Expert Answer
f left parenthesis x right parenthesis equals s g n left parenthesis x minus 1 right parenthesis H e r e comma space x minus 1 space c a n space t a k e space a n y space r e a l space v a l u e rightwards double arrow x minus 1 element of R rightwards double arrow f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 1 comma space space space space space space space x greater than 1 end cell row cell table attributes columnalign left end attributes row cell 0 comma space space space space space space x equals 1 end cell row cell negative 1 comma space space space space x less than 1 end cell end table end cell end table close A t space x equals 1 comma space f space i s space d i s c o n t i n u o u s space a s space L H L not equal to R H L space w h e n space x rightwards arrow 1 g left parenthesis x right parenthesis equals c o t to the power of negative 1 end exponent left square bracket x minus 1 right square bracket left square bracket x minus 1 right square bracket space i s space a space g r e a t e r space i n t e g e r space f u n c t i o n space a n d space t h u s space t a k e s space t h e space i n t e g e r space v a l u e s space o n l y A l s o comma space w e space k n o w space t h a t space f o r space x element of left parenthesis negative infinity comma infinity right parenthesis comma space c o t to the power of negative 1 end exponent x element of left parenthesis 0 comma straight pi right parenthesis rightwards double arrow cot to the power of negative 1 end exponent left square bracket straight x minus 1 right square bracket space is space defined space for space every space value space of space left square bracket straight x minus 1 right square bracket rightwards double arrow straight g left parenthesis straight x right parenthesis space is space continuous Since space straight f space is space discontinuous space and space straight g space is space continuous rightwards double arrow straight F left parenthesis straight x right parenthesis equals straight f left parenthesis straight x right parenthesis times straight g left parenthesis straight x right parenthesis space is space distinuous space at space straight x equals 1 Thus comma space statement space 1 space is space true Statement space 2 space is space true space and space it space is space not space the space correct space explanation space of space statement space 1.
Answered by Renu Varma | 14 May, 2019, 11:07: AM

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