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Asked by sarveshvibrantacademy | 09 May, 2019, 23:38: PM
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f left parenthesis x right parenthesis equals x over 2 minus 1 comma space x element of left square bracket 0 comma straight pi right square bracket 0 less or equal than straight x less or equal than straight pi 0 less or equal than straight x over 2 less or equal than straight pi over 2 rightwards double arrow negative 1 less or equal than straight x over 2 minus 1 less or equal than straight pi over 2 minus 1 rightwards double arrow negative 1 less or equal than f left parenthesis x right parenthesis less or equal than straight pi over 2 minus 1 S i n c e comma space tan x space i s space n o t space d e f i n e d space f o r space x equals n straight pi plus-or-minus straight pi over 2 Thus comma space tan left parenthesis straight f left parenthesis straight x right parenthesis right parenthesis space is space continuous space for space straight x element of left square bracket 0 comma straight pi right square bracket Now comma space fraction numerator 1 over denominator straight f left parenthesis straight x right parenthesis end fraction equals fraction numerator 1 over denominator begin display style straight x over 2 end style minus 1 end fraction equals fraction numerator 2 over denominator straight x minus 2 end fraction And space fraction numerator 1 over denominator straight f left parenthesis straight x right parenthesis end fraction space is space not space defined space if space straight x minus 2 equals 0 space straight i. straight e space straight x equals 2 Since space 2 element of left square bracket 0 comma straight pi right square bracket space and space fraction numerator 1 over denominator straight f left parenthesis straight x right parenthesis end fraction space is space not space defined space at space 2 Thus comma space fraction numerator 1 over denominator straight f left parenthesis straight x right parenthesis end fraction space is space not space continuous Hence comma space tan left parenthesis straight f left parenthesis straight x right parenthesis right parenthesis space is space continuous space but space fraction numerator 1 over denominator straight f left parenthesis straight x right parenthesis end fraction space is space not.
Answered by Renu Varma | 10 May, 2019, 10:51: AM

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