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Suppose functions $g$ and $f$ have the properties that $g(x)=3f^{-1}(x)$ and $f(x)=\frac{24}{x+3}$. For what value of $x$ does $g(x)=15$?

 Mar 20, 2018
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Suppose functions  \(g\)  and  \(f\)  have the properties that  \(g(x)=3f^{-1}(x)\)  and  \(f(x)=\frac{24}{x+3}\) .

For what value of  \(x\)  does  \(g(x)=15\) ?

 

 

g(x)  =  3f-1(x)

                            Since  g(x)  =  15 ,  we can plug in  15  for  g(x) .

15  =  3f-1(x)

                            Divide both sides of the equation by  3 .

5  =  f-1(x)

                            Take  f  of both sides...

f(5)  =  x

                            And  f(5)  =  \(\frac{24}{5+3}\)    so....

\(\frac{24}{5+3}\)   =   x

 

\(\frac{24}{8}\)  =  x

 

3  =  x

 Mar 20, 2018

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