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Given-f-x-2-x-2-x-2-x-2-If-g-f-x-2x-1-then-g-1-1-

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Question Number 139592 by bemath last updated on 29/Apr/21
Given f(x)=(√(2+x^2 −x)) +(√(2−x^2 )) If (g○f)(x) = 2x+1 then g^(−1) (−1)=?
Givenf(x)=2+x2−x+2−x2If(g∘f)(x)=2x+1theng−1(−1)=?
Answered by EDWIN88 last updated on 29/Apr/21
⇒(g○f)(x)= 2x+1 ; g^(−1) (2x+1)=f(x) { ((2x+1=−1⇒x=−1)),((g^(−1) (−1)=f(−1)=(√(2+1+1)) +(√(2−1)) = 3)) :}
⇒(g∘f)(x)=2x+1;g−1(2x+1)=f(x){2x+1=−1⇒x=−1g−1(−1)=f(−1)=2+1+1+2−1=3
Answered by mathmax by abdo last updated on 29/Apr/21
f(x)=(√(x^2 −x+2))+(√(2−x^2 )) gof(x)=2x+1 ⇒g(x)=f^(−1) (2x+1) ⇒g^(−1) (x)=f(2x+1) ⇒ g^(−1) (−1)=f(−1) =(√(2+1+1))+(√(2−1))=2+1=3
f(x)=x2−x+2+2−x2gof(x)=2x+1⇒g(x)=f−1(2x+1)⇒g−1(x)=f(2x+1)⇒g−1(−1)=f(−1)=2+1+1+2−1=2+1=3

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