+2862 Bro post in rendered latex please! Stop being lazy buddy!
Suppose \(f(x)=\frac{3}{2-x}\). If \(g(x)=\frac{1}{f^{-1}(x)}+9\), find \(g(3)\).
Find the inverse of function f(x). You do this by setting up f(x) as y, then switch "x" and "y". Solve for y.
.
\(y=\frac{3}{2-x}\)
\(x=\frac{3}{2-y}\)
\(2x-yx=3\)
\(2-y=\frac{3}{x}\)
\(y=-\frac{3}{x}+2\)
\(y=2-\frac{3}{x}\)
So now we figured out f-1(x). We then plug that into g(x).
\(g(x)=\frac{1}{2-\frac{3}{x}}\)
We then evaluate g(3).
I will leave that up to you now
+2862 Bro post in rendered latex please! Stop being lazy buddy!
Suppose \(f(x)=\frac{3}{2-x}\). If \(g(x)=\frac{1}{f^{-1}(x)}+9\), find \(g(3)\).
Find the inverse of function f(x). You do this by setting up f(x) as y, then switch "x" and "y". Solve for y.
.
\(y=\frac{3}{2-x}\)
\(x=\frac{3}{2-y}\)
\(2x-yx=3\)
\(2-y=\frac{3}{x}\)
\(y=-\frac{3}{x}+2\)
\(y=2-\frac{3}{x}\)
So now we figured out f-1(x). We then plug that into g(x).
\(g(x)=\frac{1}{2-\frac{3}{x}}\)
We then evaluate g(3).
I will leave that up to you now
