How do you plot the function on graph? Determine whether the function $f(x) = x^2$ is injective, surjective or bijective with reasons. Solve the recurrence relation $a_n = 6a_{n-1} + 9a_{n-2}$ with initial conditions $a_0 = 1, a_1 = 6$.[10]

A group of 8 scientist is composed of 5 chemist and 3 biologist. In how many ways can a committee of 5 be formed that has 3 chemist and 2 biologist? Using mathematical induction prove that $1^3 + 2^3 + 3^3 + ... + n^3 = (n^2(n+1)^2/4)$ for $n \geq 1$.[10]

Show that the relation R = {(a, b): |a-b| is even} is an equivalence relation in the set of integers. Given the following transport network with the edges called with their capacities find all S-D cuts and their capacities and what the minimum capacity?[10]