therefore this the answer of 1,2 and 3
(f ◦ g)(x)
This means we evaluate g(x) first, then plug that result into f(x). So, g(x) = x + 8. Then f(x + 8) = (x + 8)^2 + a(x + 8). Expanding the square gives: f(x + 8) = x^2 + 16x + 64 + 8a + ax. Therefore, (f ◦ g)(x) = x^2 + 16x + 64 + 8a + ax.
(g ◦ f)(x)
Here, we evaluate f(x) first, then plug that result into g(x). So, f(x) = x^2 + x. Then g(x^2 + x) = (x^2 + x) + 8. This simplifies to: (g ◦ f)(x) = x^2 + x + 8.
(f ◦ f)(x)
This means we evaluate f(x) twice. So, f(f(x)) = f(x^2 + x). Following the same steps from part 1, we get: (f ◦ f)(x) = x^4 + 2x^3 + x^2 + ax^2 + ax + a.
(g ◦ g)(x)
Similar to part 2, we evaluate g(x) twice. So, g(g(x)) = g(x + 8) = (x + 8) + 8 = x + 16.