Function Operations Function Composition

Function Operations Given f(x) = 2x2 + 1 and g(x) = 5x – 3 1.Find (f + g)(x) and give the domain. This could be written f(x) + g(x). 2. Find (f – g)(x) and give the domain. This could be written f(x) – g(x)

Function Operations Given f(x) = 2x2 + 1 and g(x) = 5x – 3 1.Find f(x) ∙ g(x) and give the domain. Could be written (f ∙g)(x). 2. Find f(x)/g(x) and give the domain. Could be written (f/g)(x).

Function Composition Function Composition is just fancy substitution, very similar to what we have been doing with finding the value of a function. The difference is we will be plugging in another function.

Function Composition Just the same we will still be replacing x with whatever we have in the parentheses. The notation looks like g(f(x)) or f(g(x)). We read it ‘g of f of x’ or ‘f of g of x’

Function Composition You will see (x) which is the same as f(g(x)) and (x) which is the same as g(f(x)).

Function Composition EXAMPLE Given f(x) = 2x + 2 and g(x) = 2, find f(g(x)).

Function Composition Given g(x) = x - 5 and f(x) = x + 1, find f(g(x)) and g(f(x). Give the domain.

Function Composition Given f(x) = x2 + x and g(x) = x - 4, find f(g(x)) and g(f(x)). Give the domain.

Function Composition Given f(x) = x2 + x and g(x) = x - 4, find f(g(x)) and g(f(x)). Give the domain.

Function Composition Given f(x) = 2x + 5 and g(x) = 8 + x, find f(g(-5)).

Function Composition Given f(x) = 2x + 5 and g(x) = 8 + x, find g(f(-5)).