One of the solution of the equation f(x) = g(x) for the considered functions f(x) and g(x) is given by: Option A: x = -3.5
For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)
For this case, we're given that:
The equation whose solution is to be found is:
[tex]f(x) = g(x)\\-x + 0.25 = x^2 + 3x + 2[/tex]
The solution of f(x) = g(x) is the value of x for which the outputs f(x) and g(x) come out to be same.
This solution is same to the x-value of the solution of the system of equation
[tex]y= -x+0.25\\y= x^2 + 3x + 2[/tex]
because its solution will give values of x and y for which both equations are satisfied. That means, the x-value of that solution is the value for which both the expressions [tex]x^2 + 3x + 2[/tex] and [tex]-x+ 0.25[/tex] evaluate same result (which is what we need).
The solution of the system of equation is the coordinates of the intersection of the graphs of the equations of that system.
[tex]y= -x+0.25\\y= x^2 + 3x + 2[/tex]
The graph is attached below.
That graph intersects on (x,y) = (-0.5, 0.75 ) and (x,y) = (-3.5, 3.75)
Thus, for x = -0.5, both the expressions [tex]x^2 + 3x + 2[/tex] and [tex]-x+ 0.25[/tex] evaluate same result y = f(x) = g(x) = 0.75
and for x = -3.5, both the expressions [tex]x^2 + 3x + 2[/tex] and [tex]-x+ 0.25[/tex] evaluate same result y = f(x) = g(x) = 3.75
These are the only such value as the a system of a quadratic equation and a linear equation can have at max 2 solutions.
Thus, one of the solution of the equation f(x) = g(x) for the considered functions f(x) and g(x) is given by: Option A: x = -3.5
Learn more about finding the solution graphically here:
https://brainly.com/question/26254258
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