Final answer:
The y-intercept of (f-g)(x) is -7.
Step-by-step explanation:
To find the y-intercept of the function (f-g)(x) = f(x) - g(x), we substitute x = 0 into the equation.
Using the given functions f(x) = 4x² + 2x - 5 and g(x) = -4x² - 8x + 2, we have:
(f-g)(x) = 4x² + 2x - 5 - (-4x² - 8x + 2)
= 4x² + 2x - 5 + 4x² + 8x - 2
= 8x² + 10x - 7
Substituting x = 0, we get:
(f-g)(0) = 8(0)² + 10(0) - 7
= -7
Therefore, the y-intercept of (f-g)(x) is -7.