Operations and composition of functions

Question

Find two functions f and g to express the function y = 4/(x-3) + 1 in each combination described below and prove algebraically that they create the following combinations of h(x):

a. Sum

b. Product

c. Composition

Answer 1

y= 1/(4x-3) +1 =

h(x) = f(x)+g(x)= 1/(4x-3) +1

when f(x)=1/(4x-3) and g(x)=1

h(x)=f(x)g(x) = 1/(4x-3) +1

when f(x)=1/(4x+3) and g(x)=1 +4x+3= 4x+4

h(x)= f(g(x))= 1/(4x+3)+1

when f(x)=1/x +1 and g(x)=4x-3