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Question Number 106707 by bemath last updated on 06/Aug/20
    @bemath@  Given  { ((f(x)=2x+3)),(((g○f)(x)=2x−1)) :}  find (f○g)(2).
@bemath@Given{f(x)=2x+3(gf)(x)=2x1find(fg)(2).
Answered by john santu last updated on 06/Aug/20
Answered by mathmax by abdo last updated on 06/Aug/20
f(x)=2x+3 and g(f(x)) =2x−1 ⇒g(2x+3) =2x−1  let 2x+3 =t ⇒x =((t−3)/2) ⇒g(t) =2(((t−3)/2))−1 =t−4  g(t) =t−4 ⇒fog(2) =f(g(2)) =f(−2) =−4+3 =−1 ⇒  fog(2)=−1
f(x)=2x+3andg(f(x))=2x1g(2x+3)=2x1let2x+3=tx=t32g(t)=2(t32)1=t4g(t)=t4fog(2)=f(g(2))=f(2)=4+3=1fog(2)=1

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