Unit 2B Day 2 Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is a process where one function is applied to the result of another function, denoted as (f ° g)(x) = f(g(x)).

Front

How do you calculate (f ° f)(x) for a function f(x)?

Back

To calculate (f ° f)(x), you substitute f(x) into itself, meaning you replace x in f(x) with f(x).

Front

Given f(x) = x^2 - 1, what is f(3)?

Back

f(3) = 3^2 - 1 = 9 - 1 = 8.

Front

What is the formula for the composition of two functions f(x) and g(x)?

Back

The formula for the composition of two functions is (f ° g)(x) = f(g(x)).

Front

If f(x) = 2x^2 - 1, what is f(-2)?

Back

f(-2) = 2(-2)^2 - 1 = 2(4) - 1 = 8 - 1 = 7.

Front

What does g(f(x)) represent in function composition?

Back

g(f(x)) represents the function g applied to the output of the function f at x.

Front

How do you find the value of (g ° f)(-2) if g(x) = x + 3 and f(x) = 2x^2 - 1?

Back

First, find f(-2) = 7, then find g(7) = 7 + 3 = 10, so (g ° f)(-2) = 10.

Front

What is the significance of the order of functions in composition?

Back

The order of functions in composition matters because (f ° g)(x) is generally not equal to (g ° f)(x).

Front

If f(x) = x^2 - 1 and g(x) = x + 3, what is f(g(x))?

Back

f(g(x)) = f(x + 3) = (x + 3)^2 - 1 = x^2 + 6x + 9 - 1 = x^2 + 6x + 8.

Front

What is the output of (f ° g)(x) if f(x) = 2x and g(x) = x + 1?

Back

(f ° g)(x) = f(g(x)) = f(x + 1) = 2(x + 1) = 2x + 2.