Discrete Mathematics Answers

B. Exercises: Let f(x) = x – 3 , g(x) = 2x + 1 and h(x) = x2 – 5. Find the following 1. f ₒ g 2. f ₒ h 3. h ₒ g 4. g ₒ f 5. g ₒ h 

Let f(x) = x – 3 , g(x) = 2x + 1 and h(x) = x2 – 5. Find the following 1. f ₒ g 2. f ₒ h 3. h ₒ g 4. g ₒ f 5. g ₒ h 

1. Find a relation R such that 𝑥+𝑦 2 >1 if A = {0,1, 2} and B ={0, 1, 2, 3}.

A. Try these! 1. Find a relation R such that 𝑥+𝑦 2 >1 if A = {0,1, 2} and B ={0, 1, 2, 3}. 2. Find a relation R such that y is a power of x if A = {1, 2, 3} and B = {1, 4, 5, 9} 

Let f : A → B be a function.

1. Show that for the identity function iA on A we have f ◦ iA = f.

2. Show that for the identity function iB on B we have iB ◦ f = f.

List the quadruples in the relation { a,b,c,d} where a, b, c, d are integers with

0 < a < b < c < d < 8

Find the solution of the recurrence relation an = 4an−1 − 3an−2 + 2^n + n + 3 with

a^0 = 1 and a^1 = 4.

∑j=08​(j8​)(j+1)(j+2)