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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 $g(3)$.

 May 6, 2021
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Find inverse of f(x)

 

y = (x+5)/3     switch x's and y's then solve for y

x = (y+5)/3

y = 3x -5            this is f-1(x)

 

then g ( x ) =    1  / [(3x-5) +1 ]

and g(3 ) =   1 / [ (3*3  -5) + 1] = 1/5

 May 6, 2021

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