if g(n) =2n-1 and f(n)= n^2 + n then what is g(n) + f(n)? also, state the domain and range of the resulting function.Thanks

Given the functions:

g(n)=
2n-1

f(n) = n^2 +n

We need to
find the function g(n) + f(n).

==> f(n)+ g(n)=
(f+g)(n) = 2x-1 + n^2 + n = n^2 + 3n
-1

==> (f+g)(n)= n^2 + 3n -1

The domain  = R ( all real
numbers)

To find the range, we need to
determine the maximum or minimum value of the
function.

Since the coefficient of n^2 is positive, then
the parabola facing upward. Then, the function has minimum value at the
vertex.

Now we will need to find the
vertex.

vx = -b/2a = -3/2

vy=
(f+g)(vx)= (f+g)(-3/2)= (-3/2)^2 + 3(-3/2) -1 = 9/4+9/2 -1= (9-18 - 4)/ 4 = -13/4 = -
3.25 

==> Then, the vertex is the point ( -3/2,
-3.25)

Now since the parabola is facing upward, then  the
range is all y-values such that y >=
-3.25

Then, the range is y >=
-3.25

See the graph below for further
explanation.

src="/jax/includes/tinymce/jscripts/tiny_mce/plugins/asciisvg/js/d.svg"
sscr="-7.5,7.5,-5,5,1,1,1,1,1,300,200,func,x^2 + 3x -1
,null,0,0,-7,7,black,1,none"/>