For f(x)=1-x and g(x)=2 x^{2}+x+5, find the following functions.
a. (f of g)(x)
b.(g of f)(x)
c. (f of g)(2)
d.(g of f)(2)

Step 1 ：We are given two functions, \(f(x) = 1 - x\) and \(g(x) = 2x^2 + x + 5\). We are asked to find the composite functions (f of g)(x) and (g of f)(x), and their values at x=2.

Step 2 ：The composite function (f of g)(x) is obtained by substituting \(g(x)\) into \(f(x)\). Similarly, (g of f)(x) is obtained by substituting \(f(x)\) into \(g(x)\).

Step 3 ：For (f of g)(2), we substitute x=2 into \(g(x)\) first, and then substitute the result into \(f(x)\). For (g of f)(2), we substitute x=2 into \(f(x)\) first, and then substitute the result into \(g(x)\).

Step 4 ：Calculating (f of g)(x), we substitute \(g(x)\) into \(f(x)\) to get \(f(g(x)) = 1 - (2x^2 + x + 5) = -2x^2 - x - 4\).

Step 5 ：Calculating (g of f)(x), we substitute \(f(x)\) into \(g(x)\) to get \(g(f(x)) = 2(1 - x)^2 + (1 - x) + 5 = -x + 2(1 - x)^2 + 6\).

Step 6 ：Calculating (f of g)(2), we substitute x=2 into \(g(x)\) first to get \(g(2) = 2*2^2 + 2 + 5 = 13\), then substitute 13 into \(f(x)\) to get \(f(13) = 1 - 13 = -12\).

Step 7 ：Calculating (g of f)(2), we substitute x=2 into \(f(x)\) first to get \(f(2) = 1 - 2 = -1\), then substitute -1 into \(g(x)\) to get \(g(-1) = 2*(-1)^2 - 1 + 5 = 6\).

Step 8 ：Final Answer: \n a. (f of g)(x) = \(\boxed{-2x^2 - x - 4}\) \n b. (g of f)(x) = \(\boxed{-x + 2(1 - x)^2 + 6}\) \n c. (f of g)(2) = \(\boxed{-12}\) \n d. (g of f)(2) = \(\boxed{6}\)