CBSE Class 12-science Answered

$S h o w space t h a t space t h e space d o m a i n space a n d space r a n g e space o f space t h e space f u n c t i o n comma space f open parentheses x close parentheses equals open parentheses x plus 1 close parentheses squared minus 1 comma space x greater or equal than negative 1 comma space a r e space e q u a l. space$ Please provide solution to this question

Asked by Topperlearning User | 25 Oct, 2016, 09:01: AM

Expert Answer

$C o n s i d e r space t h e space g i v e n space f u n c t i o n comma space f open parentheses x close parentheses equals open parentheses x plus 1 close parentheses squared minus 1 comma space x greater or equal than negative 1 rightwards double arrow y equals open parentheses x plus 1 close parentheses squared minus 1 rightwards double arrow y plus 1 equals open parentheses x plus 1 close parentheses squared rightwards double arrow open parentheses x plus 1 close parentheses squared equals y plus 1 rightwards double arrow x plus 1 greater or equal than square root of y plus 1 end root rightwards double arrow x greater or equal than square root of y plus 1 end root minus 1 S i n c e space x greater or equal than negative 1 comma space space d o m a i n space o f space f space i s space equals left square bracket negative 1 comma infinity right parenthesis S i n c e space x greater or equal than negative 1 comma space y plus 1 greater or equal than 0 rightwards double arrow y greater or equal than negative 1 T h u s comma space y element of left square bracket negative 1 comma infinity right parenthesis S o space r a n g e space o f space t h e space f u n c t i o n space i s space left square bracket negative 1 comma infinity right parenthesis T h u s comma space d o m a i n space a n d space r a n g e space a r e space e q u a l.$