Ok I have this problem, how do I solve?

Hello, and welcome to FMH! :)

We are given:

[MATH]f(x)=\frac{9}{x}+q[/MATH]
And we are told the point \((3,3)\) is on the graph of \(f\), thus:

[MATH]f(3)=3[/MATH]
[MATH]\frac{9}{3}+q=3[/MATH]
What then, must \(q\) be?
 
Hello, and welcome to FMH! :)

We are given:

[MATH]f(x)=\frac{9}{x}+q[/MATH]
And we are told the point \((3,3)\) is on the graph of \(f\), thus:

[MATH]f(3)=3[/MATH]
[MATH]\frac{9}{3}+q=3[/MATH]
What then, must \(q\) be?
q =9/3+3
 
Actually, I meant \(g(x)\), not the line of symmetry. Can you explain how we would go about determining the line of symmetry?
 
You can find if a shape has a Line of Symmetry by folding it. When the folded part sits perfectly on top (all edges matching), then the fold line is a Line of Symmetry.
 
We have:

[MATH]f(x)=\frac{9}{x}[/MATH]
And we can easily show that:

[MATH]f^{-1}(x)=\frac{9}{x}=f(x)[/MATH]
Thus, \(f(x)\) is an involutory function, that is it is its own inverse, and so what must its line of symmetry be?
 
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