If f(x)=2x-4 and g(x)=x(sq)+3 find each value?

Question

Problem: f(x)=2x-4 and g(x)=x(sqaured)+3 find value

(f+g)(x)

Answer 1

f(x)=2x-4
g(x)=x^2+3
f+g(x)=2x+x^2-1

Answer 2

If you are looking to find the intersection of the two equations f(x) and g(x), you would set the two equations equal to each other:
2x - 4 = x^2 + 3 subtracting 2x and adding 4 to both sides ==>
0 = x^2 - 2x + 7 you can solve this by the quadratic formula
if ax^2 + bx + c = 0 then x = [-b +- sqrt(b^2 - 4ac)] / 2a ==>
x = [-(-2) +- sqrt((-2)^2 - 4(1)(7)] / 2(1)
x = [2 +- sqrt(4 - 28)] / 2
x = [2 +- sqrt(-24)] / 2 = [2 +- sqrt(4)sqrt(-1)sqrt(6)] / 2
x = [2 +- 2i(sqrt(6))] / 2
x = 2[1 +- i(sqrt(6))] / 2
x = 1 + i(sqrt(6)) and x = 1 - i(sqrt(6))
which are imaginary numbers
The first equation graphs to a straight line through (0,-4) with positive slope 2. The second equation graphs to a parabola that has a minimum point of (0,3) that opens upward and goes through (1,4) and (-1,4) and
(2,7) and (-2,7) and
(3,12) and (-3,12)
If you graph them on the same set of axes, you will see that they do not intersect so have no real common points. The slope of the parabola at any point is g'(x) = 2x so for all points greater than (3,0) will have slope > 2(3) ==> > 6 while the slope of the line is 2. The right side of the parabola will always be steeper than the line and will not intersect the line.

If you want the equation which is the sum of the two equations
f(x) + g(x) = (2x - 4) + (x^2 + 3) = x^2 + 2x - 1 again using the
quadratic formula
x = {-(2) +- sqrt[(2^2) - 4(1)(-1)]} / 2(1)
x = [-2 +- sqrt(8)] / 2
x = [-2 +- sqrt(4)sqrt(2)] / 2
x = [-2 +- 2sqrt(2)] / 2
x = 2[-1 +- sqrt(2)] / 2
x = -1 + sqrt(2) or x = -1 - sqrt(2)
If you graph this you get a parabola whose minimum point is
(-1, -2) and goes through (0,-1) and (-2,-1) and
(1,2) and ( -3,2) and
(2,7) and (-4,7)
it intersects the x axis at the points
(-1 + sqrt(2),0) and (-1 - sqrt(2),0)
which is approximately at (.414,0) and (-3.414,0)

Answer 3

Well, f+g as a function of x will be x(square)+2x-1 which doesn't have a simple solution for x. Try a graphical representation for various values of x and see whether it represents some regular curve.