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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 25th October 2016, 9:01 AM
Answered by 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.

Answered by Expert 25th October 2016, 11:01 AM
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