Q)

Asked by araima2001 | 17th Jul, 2017, 10:30: AM

Expert Answer:

begin mathsize 16px style Consider space linear space functions space as space straight f left parenthesis straight x right parenthesis equals aX plus straight b space and space straight g left parenthesis straight x right parenthesis equals cX plus straight d.
suppose space straight f space is space increasing space and space straight g space is space decreasing.
straight f left parenthesis negative 1 right parenthesis equals negative straight a plus straight b
rightwards double arrow negative straight a plus straight b equals 0
straight f left parenthesis 1 right parenthesis equals straight a plus straight b
rightwards double arrow straight a plus straight b equals 2
straight g left parenthesis negative 1 right parenthesis equals negative straight c plus straight d
rightwards double arrow negative straight c plus straight d equals 2
straight g left parenthesis 1 right parenthesis equals straight c plus straight d
rightwards double arrow straight c plus straight d equals 0
straight h left parenthesis straight x right parenthesis equals fraction numerator straight f left parenthesis straight x right parenthesis over denominator straight g left parenthesis straight x right parenthesis end fraction equals fraction numerator straight x plus 1 over denominator 1 minus straight x end fraction
rightwards double arrow straight h open parentheses straight h open parentheses straight x close parentheses close parentheses equals fraction numerator negative 1 over denominator straight x end fraction space and space straight h open parentheses straight h open parentheses 1 over straight x close parentheses close parentheses equals negative straight x
open parentheses straight a plus 1 over straight a close parentheses squared equals straight a squared plus 2 plus 1 over straight a squared greater than 2 plus 2 equals 4
as space open parentheses straight a minus 1 over straight a close parentheses squared greater than 0 space rightwards double arrow straight a squared plus 1 over straight a squared greater than 2
rightwards double arrow open vertical bar straight h open parentheses straight h open parentheses straight x close parentheses close parentheses plus straight h open parentheses straight h open parentheses 1 over straight x close parentheses close parentheses close vertical bar equals open vertical bar straight x plus 1 over straight x close vertical bar greater than 2

NOTE colon space Similarly space you space can space prove space for space straight g space is space increasing space and space straight f space is space decreasing space function
using space straight h apostrophe left parenthesis straight x right parenthesis equals straight h open parentheses 1 over straight x close parentheses end style

Answered by Sneha shidid | 17th Jul, 2017, 11:27: AM