To find the x-intercepts of (f o g), we need to find the values of x for which (f o g)(x) = 0.
We have:
(f o g)(x) = f(g(x)) = f(4x + 10) = 2(4x + 10)^2 + 3(4x + 10) - 1
Expanding this expression, we get:
(f o g)(x) = 2(16x^2 + 80x + 100) + 12x + 29
= 32x^2 + 164x + 201
Now we need to solve the quadratic equation 32x^2 + 164x + 201 = 0 to find the x-intercepts.
We can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 32, b = 164, and c = 201.
Plugging in these values, we get:
x = (-164 ± sqrt(164^2 - 4(32)(201))) / 2(32)
≈ -2.78 and -2.05
Therefore, the x-intercepts of (f o g) are approximately -2.78 and -2.05.