Interpreting Composite Functions

Front

What is a composite function?

Back

A composite function is a function that is formed by combining two functions, where the output of one function becomes the input of the other. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you denote the composition of two functions f and g?

Back

The composition of two functions f and g is denoted as (f ∘ g)(x).

Front

What is the formula for (h ∘ g)(x) if h(x) = 4x^2 - 5x + 1 and g(x) = 8 - 7x?

Back

The formula for (h ∘ g)(x) is h(g(x)) = 4(8 - 7x)^2 - 5(8 - 7x) + 1.

Front

What is the result of (f + g)(x) if f(x) = 3x - 2 and g(x) = 8 - 7x?

Back

The result of (f + g)(x) is (3x - 2) + (8 - 7x) = -4x + 6.

Front

What do you get when you evaluate (f - g)(7) for f(x) = 3x - 2 and g(x) = 8 - 7x?

Back

You get (f - g)(7) = f(7) - g(7) = (3(7) - 2) - (8 - 7(7)) = 21 - 8 + 49 = 62.

Front

What is the difference between (f + g)(x) and (f - g)(x)?

Back

(f + g)(x) adds the outputs of f and g, while (f - g)(x) subtracts the output of g from f.

Front

How do you evaluate (g ∘ h)(x) for g(x) = 8 - 7x and h(x) = 4x^2 - 5x + 1?

Back

To evaluate (g ∘ h)(x), substitute h(x) into g: g(h(x)) = 8 - 7(4x^2 - 5x + 1).

Front

What is the output of (f ∘ g)(x) if f(x) = 3x - 2 and g(x) = 8 - 7x?

Back

The output is (f ∘ g)(x) = f(g(x)) = 3(8 - 7x) - 2 = 24 - 21x - 2 = 22 - 21x.

Front

What does it mean to evaluate a function at a specific point, such as (f)(7)?

Back

Evaluating a function at a specific point means substituting that point into the function's equation to find the output.

Front

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

Back

The order of functions in composite functions matters because (f ∘ g)(x) is not necessarily equal to (g ∘ f)(x).