Lesson 2-8: Operations of Functions

Advanced Math Topics

Operations with functions

(f + g)(x)= f(x) + g(x) Add the functions (f – g )(x) = f(x) – g(x) Subtract the functions (be sure to subtract all parts of the second function and not just the first part)

(f · g)(x) = f(x) · g(x) Multiply the functions (foil/distribute)

(f/g)(x) = f(x) / g(x), g(x) cannot = 0 Divide the functions (factor if possible and simplify)

Examples

f(x)= x2 – 3x + 1 and g(x) = 4x + 5 find – (f + g) (x) and (f – g)(x)

Example

f(x) = x2 + 5x – 1 and g(x) = 3x – 2 find– (f · g)(x) and (f/g)(x)

Composition of Functions

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

– Plug in the entire second function for every x then simplify

Example

Find [f o g](x) and [g o f](x) for f(x) = x+3 and g(x) = x2 + x – 1

Evaluate [f o g](x) and [g o f](x) for x = 2

Find the sum, difference, product and quotient of f(x) and g(x)

f(x) = x2 + 3

g(x) = x - 4

If f(x) = 3x, g(x) = x + 7 amd h(x) = x2 find the following

f[g(3)]

g[h(-2)]

h[h(1)]