Operations of Functions

Find (g/f)(x)

(g / f )(x) g(x) f (x) x2 + 5x + 6 x + 3 (x + 2)(x + 3) x + 3

Multiplication

( fg)(x) = f (x)gg(x)

Composition

[f eg](x)= f[g(x)]

Let f(x)=x+3 and g(x)=x2 +5x+6 Find (fg)(x)

( fg)(x) = f (x)gg(x) (x+3)(x2 +5x+6) x3 +5x2 +6x+3x2 +15x+18 (fg)(x)=x3 +8x2 +21x+18

Addition

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

Let f(x)=x+3 and g(x)=x2 +5x+6 Find (f+g)(x)

(f +g)(x)= f(x)+g(x) (x+3)+(x2 +5x+6) (f+g)(x)=x2 +6x+9

Subtraction

(f −g)(x)= f(x)−g(x)

Division

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

Ex: f(x) = 3x + 4 and g(x) = 6x + 8, A) Find f eg

f (g(x)) = 3x + 4 f (6x + 8) = 3x + 4 f (6x + 8) = 3(6x + 8) + 4 f (6x + 8) = 18x + 24 + 4 f (g(x)) =18x + 28

Ex: f(x) = 3x + 4 and g(x) = 6x + 8, Find [g ef ](2)

g( f (2)) = 6x + 8 g(3(2) + 4) = 6x + 8 g(10) = 6x + 8 g(10) = 6(10) + 8 g(10) = 60 + 8 g( f (2)) = 68