Prove that the graphs of the functions f(x)=2x+1 and g(x)=x^2+x+1 have a point of intersection.

The intercepting point that is located on the line
described by f(x) and parabola described by g(x), in the same time,  is the intercepting
point of the line and parabola.

So, the y coordinate of the
point verify the equation of f(x) and the equation of g(x), in the same
time.

2x+1=x^2+x+1

We'll move
all term to one side and we'll combine like
terms:

x^2-x=0

We'll factorize
by x:

x*(x-1)=0

We'll put each
factor as
zero:

x=0

x-1=0

We'll
add 1 both
sides:

 x=1

Now,
we'll substitute the value of x in the equation of the line, because it is much more
easier to compute
y.

y=2x+1

x=0

y=2*0+1,
y=1

So the first pair of coordinates of intercepting point:
M(0,1) 

x=1

y=2*1+1=3

So
the second pair of coordinates of intercepting point:
N(1,3).

So, the graphs of the functions f and
g are intercepting and their intercepting points are: M(0,1) and N(1,3).