If f (x) = x² + 3 and g (x) = 3x - 1 then find the following:

Question

1a. (f+g)(x)

1b. (f+g)(3)

1c. (f-g)(x)

1d. (fg)(x)

1e. (fg)(-1)

Answer 1

1a. (f+g)(x) = f(x)+g(x) = x^2 + 3 + 3x - 1 = x^2 + 3x + 2

1b. (f+g)(3) = 9+3+2 = 14

1c. (f-g) = x^2 - 3x + 4

1d. (fg)(x) = f(x)*g(x) = (x^2+3)(3x-1) = 3x^3 - x^2 + 9x - 3

1e. (fg)(-1) = -3 - 1 - 9 - 3 = -16