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Given the functions $f(x)=\dfrac{x+5}{3}$ and $g(x)=\dfrac{1}{f^{-1}(x)+1}$, find the value of $g(3)$.

 Dec 17, 2019
 #1
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Given the functions \(f(x)=\dfrac{x+5}{3}\) and \(g(x)=\dfrac{1}{f^{-1}(x)+1}\), find the value of g(3).

 

Hello EpicWater!

 

\(f(x)=\dfrac{x+5}{3}\\\color{blue} f^{-1}(x)=\frac{3}{x+5}\) 

\(\color{BrickRed} g(x)=\dfrac{1}{f^{-1}(x)+1}\\ g(x)=\frac{1}{\frac{3}{x+5}+1}\\ \color{BrickRed}x=3\\ g(3)=\frac{1}{\frac{3}{3+5}+1}= \frac{1}{\frac{3}{8}+1}=\frac{1}{\frac{11}{8}}\)

 

\(g(3)=\frac{8}{11}\)

 

laugh  !

 Dec 17, 2019
edited by asinus  Dec 17, 2019
edited by asinus  Dec 17, 2019
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Thank you!!!

 Dec 17, 2019

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