Find f gx f gx f gx and ln x for each fx and gx fx 8x 3

Find (f + g)(x), (f - g)(x), (f g)(x), and (l/n) (x) for each f(x) and g(x). f(x) - 8x - 3; g(x) = 4x + 5 f(x) = x^2 + x - 6; g(x) = x - 2 For each pair of functions, find f g and g f, if they exist. f = {(-1,2), (5, 6), (0, 9)}, g{(6, 0), (2, -1), (9,5)} Find [f g](x) and [g f](x), if they exist. f(x) = x^2 - 1; g(x) = -4x^2 f(x) = 5x + 4; g(x) = 3 - x

Solution

1) f(x) = 8x -3 , g(x) = 4x +5

(f + g)(x) = 8x -3 + 4x +5 = 12x +2

(f - g)(x) = 8x -3 - 4x -5 = 4x -8

(f ^. g)(x) = (8x -3)(4x +5)

==> (f ^. g)(x) = 32x² +40x -12x -15

==> (f ^. g)(x) = 32x² +28x -15

(f/g)(x) = (8x -3)/(4x +5)

2) f(x) = x² +x -6 , g(x) = x -2

==> (f +g)(x) = x² +x -6 + x -2 = x² +2x -8

==> (f -g)(x) = x² +x -6 - x +2 = x² -4

==> (f ^. g)(x) = (x² +x -6)(x -2)

==> (x² + 3x - 2x -6)(x -2) = (x(x +3) -2(x +3))(x -2)

==> (x+3)(x -2)²

==> (f ^. g)(x) = (x+3)(x -2)²

==> (f / g)(x) = (x² +x -6)/(x -2) = (x +3)(x -2)/(x -2)

==> (f / g)(x) = (x +3)