The one solution to the equation f(x) = g(x) is at option (D) x = 3.4 is the correct answer.
What is graph of a function?
A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The graph of a function f is the set of all points in the plane of the form (x, f(x)).
For the given situation,
The function f(x) = [tex]5x-2[/tex]
The function g(x) = [tex]x^{3}-2x^{2} -x+2[/tex]
The graph below shows the function f(x) and g(x).
The solution of these functions f(x) = g(x) is the point of intersection of the function.
From the graph, there are three point of intersections.
Thus there are three solutions to these functions when f(x) = g(x).
The solutions are (3.4,15), (0.5,0.9), (-2,-12)
Here the solution of x is at x = 3.4, x = 0.5 and x = -2.
Hence we can conclude that the one solution to the equation f(x) = g(x) is at option (D) x = 3.4 is the correct answer.
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