Find the following

Question

f(x) = 2x - 9, g(x) = 6 - x

(a) (f + g)(x) =

(b) (f - g)(x) =

(c) (fg)(x) =

(d) (f/g)(x) =

Answer 1

(a) (f+g) (x) = f(x) + g(x) = (2x-9) + (6-x) = 2x -9 +6 -x = x-3

(b) (f-g) (x) = f(x) - g(x) = (2x-9) - (6-x) = 2x-9-6+x =3x-15

(c) (fg) (x) = f(x)g(x) = (2x-9)(6-x) = 12x- 2x² -54 +9x = -2x²+21x-54

(d) (f/g)(x) = f(x)/g(x)= (2x-9)/(6-x)

Answer 2

Looks like your working with simple operations on functions so you need to complete the operation stated in the function.

(f + g)(x) = f(x) + g(x) = 2x - 9 + 6 - x Combine like terms and get (f + g)(x) = 2x - x - 9 + 6 = x - 3

(f - g)(x) = f(x) - g(x) = 2x - 9 -(6 - x) distribute the negative sign to get (f - g)(x) = 2x - 9 - 6 + x and combine

(f - g)(x) = 2x + x - 9 -6 = 3x -12

(fg)(x) = f(x) * g(x) = (2x - 9) * (6 - x) use FOIL to expand and get (fg)(x) = 12x - 2x² - 54 - 9x and combine and rearrange to get (fg)(x) = -2x² + 3x -54

(f/g)(x) = f(x)/g(x) = (2x - 9)/(6 - x) the equation is in simplest form