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Given-that-fog-x-2x-1-x-and-g-x-5x-2-Find-f-x-




Question Number 142052 by Rankut last updated on 26/May/21
Given that fog(x)=((2x−1)/x)  and g(x)=5x+2,  Find  f(x).
Giventhatfog(x)=2x1xandg(x)=5x+2,Findf(x).
Answered by iloveisrael last updated on 26/May/21
⇒f(5x+2)=((2x−1)/x)  ⇒f(5x+2)=2−(1/x)  ⇒f(x)=2−(1/((((x−2)/5))))=2−(5/(x−2))  ⇒f(x)=((2x−9)/(x−2))
f(5x+2)=2x1xf(5x+2)=21xf(x)=21(x25)=25x2f(x)=2x9x2
Commented by Rankut last updated on 26/May/21
how did you get (((x−2)/5))
howdidyouget(x25)
Answered by EDWIN88 last updated on 26/May/21
f(g(x))=f(5x+2)=((2x−1)/x)   let 5x+2=u⇒x=((u−2)/5)  we get f(u)=((2(((u−2)/5))−1)/((((u−2)/5))))= ((2u−4−5)/(u−2))   f(u)=((2u−9)/(u−2)) ⇒ so f(x)=((2x−9)/(x−2))
f(g(x))=f(5x+2)=2x1xlet5x+2=ux=u25wegetf(u)=2(u25)1(u25)=2u45u2f(u)=2u9u2sof(x)=2x9x2
Answered by mathmax by abdo last updated on 26/May/21
fog(x)=((2x−1)/5) ⇒f(g(x))=((2x−1)/5) ⇒f(5x+2)=((2x−1)/x)  let 5x+2=t ⇒x=((t−2)/5) ⇒f(t)=2−(1/((t−2)/5)) =2−(5/(t−2))=((2t−4−5)/(t−2))  =((2t−9)/(t−2)) ⇒f(x)=((2x−9)/(x−2))
fog(x)=2x15f(g(x))=2x15f(5x+2)=2x1xlet5x+2=tx=t25f(t)=21t25=25t2=2t45t2=2t9t2f(x)=2x9x2

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