5. For any unary function fCx), the nth iteration of f, written f*, is where f is composed with itself n times on the right side of the equation. (Note that fo(x)-x.) Let y(n, x) =f"(x). Show that if f is primitive recursive, then 1/ is also primitive recursive. 6.* (a) Let E(x) = 0 if x is even, E(x) = 1 if x is odd. Show that E(x) is primitive recursive. Let H(x) =x/2 if x is even, (x-1)/2 if x is odd. Show that H(x) is primitive recursive. (b) Let f(0)-0, f(1) = 1, f(2) = 22, f(3) = 33) = 327, etc. In general, f(n) is written as a stack n high, of n's as exponents. Show that f is primitive recursive. 7.*