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`f: RvecR ,f(x)(3x^2+m x+n)/(x^2+1)dot`If the range of this function is `[-4,3)`, then filnd the value of `|m+n|`is_________. |
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Answer» Correct Answer - 4 `f:RtoR` `f(x)=(3x^(2)+mx+n)/(x^(2)+1)` `y=(3x^(2)+mx+n)/(x^(2)+1)` `(y-3)x^(2)-mx+(y-n)=0` x must be real `=m^(2)-4(y-3)(y-n)ge0` `=4(y-3)(y-n)-m^(2)le0` `=(y-3)(y-n)-(m^(2))/(4)le0` As range in `[-4,3]` `y^(2)-(3+n)y+3n-(m^(2))/(4)=(y+4)(y-3)=y^(2)+y-12` `=(-3+n)=1impliesn=-4` `=3n-(m^(2))/(4)=-12` `=m=0` `=y^(2)-(3+n)y+3n-(m^(2))/(4)=(y+4)(y-3)-y^(2)+y-12` `=-(3+n)=1impliesn-4` `3n-(m^(2))/(4)=-12` `m=0` |
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