Final answer:
To find the domain for which the functions f(x)=2x^2-1 and g(x)=1-3x are equal, we set the two functions equal to each other and solve for x using the quadratic formula. The solutions are x = 1/2 or x = -2.
Step-by-step explanation:
To find the domain for which the functions f(x)=2x^2-1 and g(x)=1-3x are equal, we need to set the two functions equal to each other and solve for x.
2x^2-1 = 1-3x
Combine like terms: 2x^2 + 3x - 2 = 0
Now, we can use the quadratic formula to solve for x: x = (-b ± sqrt(b^2 - 4ac)) / 2a. Plugging in the values: x = (-3 ± sqrt(3^2 - 4(2)(-2))) / (2(2)).
Simplifying further, we get: x = (-3 ± sqrt(9 + 16)) / 4. x = (-3 ± sqrt(25)) / 4. x = (-3 ± 5) / 4. This gives us two solutions: x = 2/4 or x = -8/4. Simplifying, we have x = 1/2 or x = -2.
Therefore, the domain for which the functions f(x) and g(x) are equal is x = 1/2 or x = -2.