Question

Use the graph that shows the solution to f(x)=g(x). f(x)=2x√3−4 g(x)=2x2−4 What is the solution to f(x)=g(x)? Select each correct answer. Responses x=−1 x equals negative 1 x = 0 x, = 0 x = 1 x, = 1 x = 2

Answer 1

To find the solutions to f(x) = g(x), set the two functions equal to each other, rearrange the equation, and use the quadratic formula to solve for x.

To find the solution to f(x) = g(x), we need to set the two functions equal to each other and solve for x. So, we have:

2x√3 - 4 = 2x^2 - 4

Rearrange the equation:

2x^2 - 2x√3 = 0

Now, we can use the quadratic formula to solve for x:

x = (-(-2x√3) ± √((-2x√3)^2 - 4(2)(0))) / (2(2))

Simplify the equation:

x = (2x√3 ± √(12x^2 - 4(2)(0))) / 4

Simplify further:

x = (x√3 ± √(3x^2)) / 2

So, the solutions to f(x) = g(x) are x = x√3 / 2 and x = -x√3 / 2.