Question

Let f and g be the functions from the set of integers to the set of integers defined by f (x) = 2x + 3 and g(x) = 3x + 2. What is the composition of f and g? g and f ?

Answer 1

Answer:

1. f(g(x))= 6x + 7

2. g(f(x))= 6x + 11

Step-by-step explanation:

Given: f(x)= 2x+3

           g(x) = 3x+2

to find: f(g(x)) and g(f(x))

solution: 1. f(g(x)) simply means the value of g(x) in the variable of f(x)

                  therefore, putting 3x + 2 in place of x (variable) of f(x)

                   i.e 2(3x+2) + 3 = 6x + 7

               2. g(f(x)) simply means the value of f(x) in the variable of g(x)

                  therefore, putting 2x + 3 in place of x (variable) of g(x)

                   i.e 3(2x+3) + 2 = 6x + 11

Answer 2

Answer:

b) Solve the recurrence relation a n -6a n - 1 +8a n-2 =3^ n where a_{0} = 3 and a_{1} = 7 .