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 $g(x)=15$?
+9467 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
