Calculate (f+g) and fg

Question

Calculate (f+g) and fg

f(x) = x^2+2x-2

g(x) = 2/(x-3)

Answer 1

by f+g i'm assuming you mean, f(x) + g(x). So that would be x² + 2x -2 + (2/(x+3)) = ([(x² + 2x - 2)*(x+3)] + [2])/ (x+3) = (x³+2x²-2x +3x² + 6x - 6 + 2)/(x+3) = (x³ + 5x² + 4x - 4)/(x+3)

fg = f(g(x)) = (2/(x+3))^2 + 2(2/(x+3)) - 2 ... it's a little difficult to type out the full response, but just evaluate. We're substituting g(x) in for x in the f(x) function. Let me know if you need clarification.