Answer:
Explanation:
To find the value of x such that f(x) = g(x), we need to set the two functions equal to each other and solve for x.
First, let's define the variables:
f(x) = 2x² - x - 6 is a quadratic function with x as the variable.
g(x) = x² - 4 is also a quadratic function with x as the variable.
Now, to find the value of x such that f(x) = g(x), we set the two functions equal to each other:
2x² - x - 6 = x² - 4
Next, we simplify this equation by subtracting x² from both sides:
x² + x - 10 = 0
This is a quadratic equation, which we can solve for x using either the quadratic formula or by factoring.
Let's try factoring:
x² + x - 10 = (x + 5)(x - 2) = 0
So either x + 5 = 0 or x - 2 = 0. Solving for x, we find that:
x = -5 or x = 2
These are the two values of x such that f(x) = g(x).