Composition of Functions with Graphs and Tables

Front

What is a function composition?

Back

Function composition is the process of applying one function to the results of another function. If you have two functions, f(x) and g(x), the composition is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you evaluate h(f(-2)) if h(x) = 2x and f(x) = x + 2?

Back

First, find f(-2): f(-2) = -2 + 2 = 0. Then, find h(0): h(0) = 2(0) = 0.

Front

What is the notation for function composition?

Back

The notation for function composition is (f ∘ g)(x), which means f(g(x)).

Front

If f(x) = 3x + 10, what is f(2)?

Back

f(2) = 3(2) + 10 = 6 + 10 = 16.

Front

What is the result of f(g(5)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

g(5) = 5 - 2 = 3. Then, f(g(5)) = f(3) = 3(3) + 10 = 9 + 10 = 19.

Front

How do you find h(f(g(-2))) if h(x) = -3x, f(x) = x^2 - 2, and g(x) = x + 9?

Back

First, find g(-2): g(-2) = -2 + 9 = 7. Then, find f(7): f(7) = 7^2 - 2 = 49 - 2 = 47. Finally, find h(47): h(47) = -3(47) = -141.

Front

What is the composition of functions f(x) = x^2 and g(x) = 1/x^2?

Back

The composition (f ∘ g)(x) = f(g(x)) = f(1/x^2) = (1/x^2)^2 = 1/x^4.

Front

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

Back

(f ∘ g)(-1) = f(g(-1)) = f(1/(-1)^2) = f(1) = 1^2 = 1.

Front

What is the domain of the function g(x) = 1/x?

Back

The domain of g(x) = 1/x is all real numbers except x = 0.

Front

What does it mean for a function to be undefined?

Back

A function is undefined at points where the input does not produce a valid output, such as division by zero.