Composite Functions & Operations

Front

What is a composite function?

Back

A composite function is a function that is formed by combining two functions, denoted as (f∘g)(x) = f(g(x)).

Front

How do you find (f - g)(x) for two functions f(x) and g(x)?

Back

To find (f - g)(x), subtract the expression of g(x) from f(x): (f - g)(x) = f(x) - g(x).

Front

What is the formula for (f + g)(x)?

Back

The formula for (f + g)(x) is the sum of the two functions: (f + g)(x) = f(x) + g(x).

Front

How do you evaluate (f∘g)(x)?

Back

To evaluate (f∘g)(x), first find g(x) and then substitute that result into f: (f∘g)(x) = f(g(x)).

Front

What does g(f(x)) represent?

Back

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

Front

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

Back

(f - g)(x) is the difference of the two functions, while (f + g)(x) is the sum of the two functions.

Front

If f(x) = 3x + 10, what is f(0)?

Back

f(0) = 3(0) + 10 = 10.

Front

If g(x) = x - 2, what is g(0)?

Back

g(0) = 0 - 2 = -2.

Front

What is the result of (g(x) / f(x))?

Back

The result of (g(x) / f(x)) is the ratio of the two functions: (g(x) / f(x)) = (x - 2) / (x + 3).

Front

How do you find the value of (f∘g)(0) if f(x) = 3x + 10 and g(x) = x - 2?

Back

First, find g(0) = -2, then find f(-2) = 3(-2) + 10 = 4.