Which is the correct option? If begin mathsize 12px style f open parentheses x close parentheses equals sin x plus cos x comma g open parentheses x close parentheses equals x squared minus 1 comma t h e n space g open parentheses f open parentheses x close parentheses close parentheses space i s space i n v e r t i b l e space i n space t h e space d o m a i n
i. open square brackets 0 comma straight pi over 2 close square brackets space space space space space space i i. open square brackets negative straight pi over 4 comma straight pi over 4 close square brackets space space space space space space i i i. open square brackets fraction numerator negative straight pi over denominator 2 end fraction comma straight pi over 2 close square brackets space space space space space space i v. open square brackets 0 comma straight pi close square brackets end style

Asked by sunil2791 | 11th Jun, 2017, 11:41: AM

Expert Answer:

begin mathsize 16px style straight f left parenthesis straight x right parenthesis equals sinx plus cosx
straight g left parenthesis straight x right parenthesis equals straight x squared minus 1
rightwards double arrow straight g open parentheses straight f open parentheses straight x close parentheses close parentheses equals straight g open parentheses sinx plus cosx close parentheses
rightwards double arrow straight g open parentheses straight f open parentheses straight x close parentheses close parentheses equals open parentheses sinx plus cosx close parentheses squared minus 1
rightwards double arrow straight g open parentheses straight f open parentheses straight x close parentheses close parentheses equals 2 sinxcosx
rightwards double arrow straight g open parentheses straight f open parentheses straight x close parentheses close parentheses equals sin 2 straight x
minus 1 less or equal than sinθ less or equal than 1
rightwards double arrow negative 1 less or equal than sin 2 straight x less or equal than 1
rightwards double arrow sin to the power of negative 1 end exponent open parentheses negative 1 close parentheses less or equal than 2 straight x less or equal than sin to the power of negative 1 end exponent open parentheses 1 close parentheses
rightwards double arrow negative straight pi over 2 less or equal than 2 straight x less or equal than straight pi over 2
rightwards double arrow negative straight pi over 4 less or equal than straight x less or equal than straight pi over 4 end style

Answered by Sneha shidid | 12th Jun, 2017, 09:37: AM