Composition of Functions with Graphs and Tables

Front

What is the composition of functions?

Back

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

Front

How do you evaluate a composition of functions?

Back

To evaluate a composition of functions, substitute the input value into the innermost function and then use the result as the input for the outer function.

Front

What is the notation for the composition of functions?

Back

The notation for the composition of functions is f(g(x)), which means 'apply g to x, then apply f to the result of g(x)'.

Front

If f(x) = 2x + 3 and g(x) = x - 1, what is f(g(4))?

Back

f(g(4)) = f(4 - 1) = f(3) = 2(3) + 3 = 9.

Front

What is the value of h(g(-3)) if h(x) = x and g(x) = x?

Back

h(g(-3)) = h(-3) = -3.

Front

How do you find f(f(x)) for a given function f?

Back

To find f(f(x)), substitute f(x) into itself. For example, if f(x) = 2x, then f(f(x)) = f(2x) = 2(2x) = 4x.

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). The output of one function becomes the input of the next.

Front

If g(a) = 4a + 1 and h(a) = -3a + 2, how do you find g(h(1))?

Back

First, find h(1) = -3(1) + 2 = -1. Then, substitute -1 into g: g(-1) = 4(-1) + 1 = -3.

Front

What is the output of g(f(2)) if f(x) = x + 3 and g(x) = 2x?

Back

g(f(2)) = g(2 + 3) = g(5) = 2(5) = 10.

Front

What is the relationship between the graphs of two functions f and g when composing them?

Back

The graph of the composition f(g(x)) can be visualized as applying the transformation of g first, followed by the transformation of f.