Question

Solvef(x) = 2x - 13g(x) = x^2 - 6x + 3

Answer 1

The given system of functions is:

`\begin{gathered} f(x)=2x-13 \\ g(x)=x^2-6x+3 \end{gathered}`

The solution to this system is given by:

`f(x)=g(x)`

Replace the functions and solve for x, as follows:

`\begin{gathered} 2x-13=x^2-6x+3 \\ \text{ Subtract 2x from both sides} \\ 2x-2x-13=x^2-6x-2x+3 \\ -13=x^2-8x+3 \\ \text{ Add 13 to both sides} \\ -13+13=x^2-8x+3+13 \\ 0=x^2-8x+16 \end{gathered}`

Now, apply the quadratic formula to find the x-values:

`\begin{gathered} \text{ The function is writen in the form} \\ ax^2+bx+c=0 \\ a=1,b=-8,c=16 \\ \text{ The quadratic function is} \\ x=(-b\pm√(b^2-4ac))/(2a) \\ \\ x=(-(-8)\pm√((-8)^2-4(1)(16)))/(2(1)) \\ \\ x=(8\pm√(64-64))/(2) \\ \\ x=(8\pm√(0))/(2) \\ \\ x=(8\pm0)/(2) \\ \\ x=(8)/(2) \\ \\ x=4 \end{gathered}`

Then, the solution is x=4.

Let's check:

`\begin{gathered} f(4)=2*4-13=8-13=-5 \\ g(4)=4^2-6*4+3=16-24+3=18-24=-5 \\ f(4)=g(4)=-5 \end{gathered}`

The answer is x=4.