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3 will thumbs up!

Jun 4, 2018

#1
+2

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

Jun 4, 2018
#2
+1

Thanks os much for this, but what would it look like if we did a table of values?

Guest Jun 4, 2018
#3
+1

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 :)

Jun 4, 2018