please help :(

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,

 

Gavin

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

 

f(x)=x^2-6x+8

x	0	1	2	3	4	5
f(x)	0-0+8=8	1-6+8=3	2^2-6*2+8 =4-12+8 =0	etc

 

g(x)=x-2

x	0	1	2	3	4	5
g(x)	0-2=2	1-2=-1	2-2=0	etc

 

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 :)