Question

The graph points are : g(x) = 3x + 2mf(x) = |x-1| + 1

Answer 1

We are given the following system of equations:

`\begin{gathered} g(x)=3x+2 \\ f(x)=|x-1|+1 \end{gathered}`

A solution of the system is the value of "x" for which:

`g(x)=f(x)`

This means the point where the functions yield the same number. To determine if the point:

`(x,y)=(1,5)`

This means that we need to substitute the value x = 1 and both functions must be equal to 5. Substituting in g(x) we get:

`g(1)=3(1)+2=3+2=5`

Now we substitute in the function f(x):

`f(1)=|1-1|+1=0+1=1`

Since:

`g(1)\\e f(1)\\e5`

This point is not a solution of the system.