Please help 9 Let fx 2x 3 gx x 2 and hx 2x2 x 6 Write

Please help. 9

Let f(x) = 2x - 3, g(x) =x + 2, and h(x) = 2x^2 + x - 6. Write a formula for each of the following functions. (fh)(x) = (h/f) (x) = (h/g)(x) =

Solution

f(x) = 2x - 3

g(x) = x+2

h(x) = 2x^2 + x - 6

a) (fh)(x)

(fh)(x) = f(x) * h(x) = (2x-3)(x^2 + x - 6 ) = 2x^3 + 2x^2 - 12x - 3x^2 - 3x + 18

(fh)(x) = 2x^3 - x^2 - 15x + 18

b) (h/f)(x) = h(x) / f(x) = 2x^2 + x - 6 / 2x- 3

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

(h/f)(x) = (x+2)

c) ( h/g)(x) = h(x) / g(x) = 2x^2 + x - 6 / (x+2)

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

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