Q)

Asked by araima2001 | 28th Jan, 2017, 08:58: PM

Expert Answer:

begin mathsize 16px style Given space that space sin to the power of negative 1 end exponent straight x equals open vertical bar straight x minus straight a close vertical bar
We space know space that space sin to the power of negative 1 end exponent straight x element of open square brackets negative straight pi over 2 comma straight pi over 2 close square brackets space space space and space straight x element of open square brackets negative 1 comma 1 close square brackets comma space that space is space minus 1 less or equal than straight x less or equal than 1
left right double arrow negative straight pi over 2 less or equal than sin to the power of negative 1 end exponent straight x less or equal than straight pi over 2
left right double arrow negative straight pi over 2 less or equal than open vertical bar straight x minus straight a close vertical bar less or equal than straight pi over 2
left right double arrow open vertical bar straight x minus straight a close vertical bar less or equal than straight pi over 2
Using space open vertical bar straight x minus straight a close vertical bar less or equal than straight r comma space left right double arrow negative straight r space less or equal than straight x minus straight a less or equal than straight r comma space we space get
minus straight pi over 2 less or equal than straight x minus straight a less or equal than straight pi over 2
Multiplying space by space minus 1 space throughout comma space we space get
straight pi over 2 greater or equal than straight a minus straight x greater or equal than negative straight pi over 2
rightwards double arrow straight x plus straight pi over 2 greater or equal than straight a greater or equal than straight x minus straight pi over 2 space.... left parenthesis Adding space straight x space throughout right parenthesis
rightwards double arrow straight x minus straight pi over 2 less or equal than straight a less or equal than straight x plus straight pi over 2
Now comma space since space the space domain space of space sin to the power of negative 1 end exponent straight x space is space left square bracket negative 1 comma 1 right square bracket comma space
rightwards double arrow 1 minus straight pi over 2 less or equal than straight a less or equal than 1 plus straight pi over 2

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Answered by Rebecca Fernandes | 30th Jan, 2017, 12:48: PM