Question Number 148911 by mathdanisur last updated on 01/Aug/21

f:[−3, 0]→[7, 22] f(x) = x^2 - 2x + 7 find f^( −1) (x) = ?

Answered by EDWIN88 last updated on 01/Aug/21

f is one−one since f(x_1 )=f(x_2 ) ⇒x_1 ^2 −2x_1 +7=x_2 ^2 −2x_2 +7 ⇒(x_1 −x_2 )(x_1 +x_2 )−2(x_1 −x_2 )=0 ⇒(x_1 −x_2 )(x_1 +x_2 −2)=0 ⇒x_1 =x_2 [ ∵ x_1 +x_2 −2 ≠ 0 ] let y∈Y then f being onto there exist x such that y=f(x) Now y=f(x)=x^2 −2x+7 y=(x−1)^2 +6 ⇒x=1+(√(y−6)) ⇒f^(−1) (y)=1+(√(y−6)) thus we define f^(−1) (x)=1+(√(x−6))

Commented bymathdanisur last updated on 01/Aug/21

Thank you Ser