Question Number 103457 by bobhans last updated on 15/Jul/20

f(((1−x)/(1+x))) = x+2 then what is the domain and range of f^(−1) (x) ?

Answered by Worm_Tail last updated on 15/Jul/20

f(((1−x)/(1+x)))=x+2 (((1−x)/(1+x)))=f^(−1) (x+2)_(x=x−2) ((3−x)/(−1+x))=f^(−1) (x) Domain=R−{1} 3−x=−f^(−1) (x)+xf^(−1) (x) x=((3+f^(−1) (x))/(1+f^(−1) (x))) Range=R−{−1}

Answered by bemath last updated on 15/Jul/20

f^(−1) (x+2) = ((1−x)/(1+x)) f^(−1) (x) = ((1−(x−2))/(1+x−2)) = ((3−x)/(x−1))=((−x+3)/(x−1)) domain f^(−1) (x) ⇒ x∈R∧x≠1 for find Range f^(−1) (x) ⇔x = ((f^(−1) (x)+3)/(f^(−1) (x)+1)) ; range :y∈R∧y≠−1