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Question Number 93898 by mathmax by abdo last updated on 16/May/20

let f(x)=2(√(3−x)) and g(x) =x^2 −2x +5  1) calculate fog(x) and determine D_(fog)   2) calculate  ∫ fog(x)dx  3) calculate ∫ ((f^(−1) (x))/(f(x)))dx  and  ∫ ((f^(−1) og(x))/(fog(x)))dx

letf(x)=23xandg(x)=x22x+51)calculatefog(x)anddetermineDfog2)calculatefog(x)dx3)calculatef1(x)f(x)dxandf1og(x)fog(x)dx

Commented by mathmax by abdo last updated on 17/May/20

sorry g(x) =x^2 −2x−5

sorryg(x)=x22x5

Answered by Kunal12588 last updated on 16/May/20

1⟩ fog(x)=2(√(3−x^2 +2x−5))=2(√(2x−x^2 −2))  what is meant by D_(fog) ?(derivative?)  2⟩ 2∫(√(−[(x−1)^2 +2−1])) dx       =2∫(√(−(x−1)^2 −1)) dx  it is like finding ∫(√(−x)) dx; I hvn′t learnt  about complex integrals.  3⟩ f^(−1) (x)=3−(x^2 /2)=(1/2)(12−x^2 )  I=(1/4)∫((12−x^2 )/(√(3−x)))dx       (√(3−x))=t⇒ x=3−t^2 ⇒ dx=−2t dt  I=(1/4)∫((12−(3−t^2 )^2 )/t)(−2t)dt    =(1/2)∫[(t^2 −3)^2 −12] dt=(1/2)∫(t^4 −6t^2 −3)dt    =(1/(10))(3−x)^2 (√(3−x))−(3−x)(√(3−x))−(3/2)(√(3−x))+C  =(1/(10))(x^2 −5x−9)(√(3−x))+C  4⟩ complex integral

1fog(x)=23x2+2x5=22xx22whatismeantbyDfog?(derivative?)22[(x1)2+21]dx=2(x1)21dxitislikefindingxdx;Ihvntlearntaboutcomplexintegrals.3f1(x)=3x22=12(12x2)I=1412x23xdx3x=tx=3t2dx=2tdtI=1412(3t2)2t(2t)dt=12[(t23)212]dt=12(t46t23)dt=110(3x)23x(3x)3x323x+C=110(x25x9)3x+C4complexintegral

Commented by mathmax by abdo last updated on 17/May/20

thank you kunal

thankyoukunal

Commented by mathmax by abdo last updated on 17/May/20

D_(fog)  mean set of definition..!

Dfogmeansetofdefinition..!

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