I believe we don't need to use a table of values.
The question is saying, when you plug a number, \(x\), into the two functions, the two results are the same.
Let's call the number, \(n\).
When we plug \(n\) into \(f(x)\), we get \(n^2 - 6n + 8.\)
When we plug \(n\) into \(g(x)\), we get \(n - 2\)
The problem states that these two values are equal, so we can write the equation:
\(n^2-6n+8=n-2\\ n^2-7n+10=0\\ (n-5)(n-2)=0\\ n_1=5\ n_2=2\)
I hope this helped,
The reason Gavin did it his way is that most times this would not work for a table of values.
You would not be able to pick the exact right x value to put into the table. BUT this one has been chosen so that it is easy.
f(x)=x^2-6x+8 this is a parabola, maybe you are meant to know that
g(x)=x-2 this is a line and maybe you are meant to know that as well.
There will be at most two points of intersection between a line and a parabola, lets see if we can find them
I can see that for x=2 f(2)=0 and g(2)=0
so f(x)=g(x) when x=2 So the first solution is x=2
Now continue the tables and see if you can find another match :)