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Question Number 184739 by SLVR last updated on 11/Jan/23
Number of linear functions be defined f:[−1, 1]→[0,2] is a)1 b)2 c)3 d)4
Numberoflinearfunctionsbedefinedf:[−1,1]→[0,2]isa)1b)2c)3d)4
Commented by SLVR last updated on 11/Jan/23
kindly help me..answer says 2 only..how
kindlyhelpme..answersays2only..how
Answered by mr W last updated on 11/Jan/23
in domain [−1,1] the linear function f(x)=ax+b has the range [−a+b,a+b] if a>0 (case 1) or [a+b,−a+b] if a<0 (case 2) since the range should be [0,2], case 1: −a+b=0 a+b=2 ⇒a=1, b=1 ⇒f(x)=x+1 case 2: a+b=0 −a+b=2 ⇒a=−1, b=1 ⇒ f(x)=−x+1 i.e. there are 2 functions satisfying the given conditions: f(x)=x+1 or f(x)=−x+1
indomain[−1,1]thelinearfunctionf(x)=ax+bhastherange[−a+b,a+b]ifa>0(case1)or[a+b,−a+b]ifa<0(case2)sincetherangeshouldbe[0,2],case1:−a+b=0a+b=2⇒a=1,b=1⇒f(x)=x+1case2:a+b=0−a+b=2⇒a=−1,b=1⇒f(x)=−x+1i.e.thereare2functionssatisfyingthegivenconditions:f(x)=x+1orf(x)=−x+1
Commented by SLVR last updated on 11/Jan/23
So great of you sir... so kind of you sir..Thanks again
Sogreatofyousir…sokindofyousir..Thanksagain

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