Question

Enter your answer and show all the steps that you use to solve this problem in the space provided.

Let f(x)=(x2+3x−4)
and g(x)=(x+4)

a. Find f⋅g
and state the domain.
b. Find fg
and state the domain.

Answer 1

[AI-generated answer — Bot GPT 3.5]

a. To find f⋅g, we multiply the two functions together:

f⋅g = (x^2 + 3x - 4)(x + 4)
f⋅g = x^3 + 4x^2 + 3x^2 + 12x - 4x - 16
f⋅g = x^3 + 7x^2 + 8x - 16

The domain of f⋅g is the set of all real numbers.

b. To find fg, we multiply the two functions together:

fg = (x^2 + 3x - 4)/(x + 4)
fg = (x - 1)(x + 4)/(x + 4)
fg = x - 1

The domain of fg is all real numbers except x = -4.