Question

Consider the two functions:

Answer 1

Answer:

Step-by-step explanation:

1, Find (g-f)(x)

we know (g-f)(x) = g(x) - f(x) = ( 5x -2) -( 2x^2 +3x +6)

= 5x -2 - 2x^2 - 3x - 6

= -2x^2 + 2x -8

So the function (g-f)(x) = - 2x^2 + 2x - 8

2, Find (fg)(x)

we know that (fg)(x) = f(x) * g(x)

= (2x^2 +3x +6 ) *( 5x -2)

= 5x* (2x^2 +3x +6 ) - 2*(2x^2 +3x +6 )

= 10x^3 + 15x^2 +30x -4x^2 -6x - 12

= 10x^3 + 11x^2 + 24x - 12

The answer is (fg)(x)= = 10x^3 + 11x^2 + 24x - 12