Given the functions fx 6 x and gx 3x 2 sketch the graph

Given the functions f(x) = 6 - x and g(x) = 3x + 2, sketch the graph of h(x) for each question below and state the domain and range. h(x) = g(x) - f(x) h(x) = (g/f)(x)

Solution

a. f(x) = 6-x

    g(x) = 3x+2

   h(x) = g(x) - f(x) = 3x+2-6+x= 4x-4

Here there is no restriction on x and y. Hence the domain and range both are (-inf,inf)

b. h(x)= (g/f)(x) (3x+2)/(6-x)

The bottom cant be zero and at x=6 the bottom becomes zero. Hence the domain is (-inf,6)U(6,inf). range is (-inf,3)U(3,inf)