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If-f-x-x-2-2x-8-x-2-7x-12-then-find-f-1-x-

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Question Number 165687 by mnjuly1970 last updated on 06/Feb/22
If f(x)= ((x^( 2) − 2x −8)/(x^( 2) −7x +12)) then ,find : f^( −1) (x)=?
Iff(x)=x2−2x−8x2−7x+12then,find:f−1(x)=?
Answered by TheSupreme last updated on 07/Feb/22
D=R−{4,3} f(x)=(((x−4)(x+2))/((x−4)(x−3)))=((x+2)/(x−3))=1+(5/(x−3)) y−1=(5/(f^− (y)−3)) f^(−1) (y)=3+(5/(y−1))
D=R−{4,3}f(x)=(x−4)(x+2)(x−4)(x−3)=x+2x−3=1+5x−3y−1=5f−(y)−3f−1(y)=3+5y−1
Answered by Rasheed.Sindhi last updated on 06/Feb/22
f(x)= ((x^( 2) − 2x −8)/(x^( 2) −7x +12))=(((x−4)(x+2))/((x−4)(x−3))) y= ((x+2)/(x−3))=((x−3+5)/(x−3))=1+(5/(x−3)) y−1=(5/(x−3)) x−3=(5/(y−1))⇒x=(5/(y−1))+3=((3y−3+5)/(y−1)) x=((3y+2)/(y−1)) Exchanging x & y y=((3x+2)/(x−1)) ∴ f^(−1) (x)=((3x+2)/(x−1))
f(x)=x2−2x−8x2−7x+12=(x−4)(x+2)(x−4)(x−3)y=x+2x−3=x−3+5x−3=1+5x−3y−1=5x−3x−3=5y−1⇒x=5y−1+3=3y−3+5y−1x=3y+2y−1Exchangingx&yy=3x+2x−1∴f−1(x)=3x+2x−1

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