Question

Graph y=f(x) and y=g(x) on the set of axes below. f(x)=2x^2-8x+3 g(x)=-2x+3. I found that answer but I don’t know how to find the next thing they are asking for which is, Determine and state all values of x for which f(x)=g(x)

Answer 1

Given:

f(x) = 2x²-8x+3

g(x) = -2x+3

The objective is to find all values of x for which f(x) = g(x).

To find the values of x, equate the given functions.

$\begin{gathered} f(x)=g(x) \\ 2x^2-8x+3=-2x+3 \\ 2x^2-8x+3+2x-3=0 \\ 2x^2-6x=0 \\ 2x(x-3)=0 \end{gathered}$

On solving the above equation,

$\begin{gathered} 2x=0 \\ x=\frac{0}{2} \\ x=0 \end{gathered}$

Similarly,

$\begin{gathered} x-3=0 \\ x=3 \end{gathered}$

Hence, the values of x are 0 and 3.