6-1: Operations on Functions (Composition of Functions)

I can find the composition of functions

Composition of functions

Putting one function into another function

Composition of functions

Putting one function into another function

Two ways of writing: f₀g(x) = f(g(x))

Composition of functions

Putting one function into another function

Two ways of writing: f₀g(x) = f(g(x))Replace the “x” in f(x) with “g(x)”

Ex: f(x) = 2x – 5 g(x) = 4x

Ex: f(x) = 2x – 5 g(x) = 4x

f₀g(x) =

Ex: f(x) = 2x – 5 g(x) = 4x

f₀g(x) = f(g(x))

Ex: f(x) = 2x – 5 g(x) = 4x

f₀g(x) = f(g(x)) = f(4x)

Ex: f(x) = 2x – 5 g(x) = 4x

f₀g(x) = f(g(x)) = f(4x) = 2( ) – 5

Ex: f(x) = 2x – 5 g(x) = 4x

f₀g(x) = f(g(x)) = f(4x) = 2(4x) – 5

Ex: f(x) = 2x – 5 g(x) = 4x

f₀g(x) = f(g(x)) = f(4x) = 2(4x) – 5 = 8x – 5

Ex: f(x) = 2x – 5 g(x) = 4x

f₀g(x) = f(g(x)) = f(4x) = 2(4x) – 5 = 8x – 5

g₀f(x)

Ex: f(x) = 2x – 5 g(x) = 4x

f₀g(x) = f(g(x)) = f(4x) = 2(4x) – 5 = 8x – 5

g₀f(x) = g(f(x)) =

Ex: f(x) = 2x – 5 g(x) = 4x

f₀g(x) = f(g(x)) = f(4x) = 2(4x) – 5 = 8x – 5

g₀f(x) = g(f(x)) = 4( )

Ex: f(x) = 2x – 5 g(x) = 4x

f₀g(x) = f(g(x)) = f(4x) = 2(4x) – 5 = 8x – 5

g₀f(x) = g(f(x)) = 4(2x – 5)

Ex: f(x) = 2x – 5 g(x) = 4x

f₀g(x) = f(g(x)) = f(4x) = 2(4x) – 5 = 8x – 5

g₀f(x) = g(f(x)) = 4(2x – 5) = 8x – 20

HW: 27-49 all, 52-54 all