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Suppose f(x)=\frac{3}{2-x}. If g(x)=\frac{1}{f^{-1}(x)}+9, find g(3).

 Nov 7, 2019

Best Answer 

 #1
avatar+2551 
+3

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

 Nov 7, 2019
edited by CalculatorUser  Nov 7, 2019
 #1
avatar+2551 
+3
Best Answer

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

CalculatorUser Nov 7, 2019
edited by CalculatorUser  Nov 7, 2019

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