Option C: [tex]x=2[/tex] is the solution of the graph.
Explanation:
The function is [tex]f(x)=-\frac{3}{4}x^{2} +3x+1[/tex] and [tex]g(x)=2x[/tex]
We need to determine the solution of the function.
The solution can be determined by equating [tex]f(x)=g(x)[/tex]
Thus, we have,
[tex]-\frac{3}{4}x^{2} +3x+1=2x[/tex]
Subtracting both sides by 2x, we have,
[tex]-\frac{3}{4}x^{2} +x+1=0[/tex]
Multiplying both sides by 4, we have,
[tex]-3x^{2} +4x+4=0[/tex]
Factoring, we get,
[tex]-3x^{2} +6x-2x+4=0[/tex]
Factoring out the common terms, we have,
[tex](-3x^{2} +6x)+(-2x+4)=0[/tex]
Simplifying, we get,
[tex]-3x(x-2)-2(x-2)=0[/tex]
[tex](-3x-2)(x-2)=0[/tex]
Thus, we have,
[tex]-3x-2=0[/tex] or [tex]x-2=0[/tex]
Simplifying, we get,
[tex]x=-\frac{2}{3}[/tex] or [tex]x=2[/tex]
Thus, the solution of the graph is [tex]x=2[/tex]
Therefore, Option C is the correct answer.
