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)?

Back

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

Front

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

Back

The product of two functions is given by (f*g)(x) = f(x) * g(x).

Front

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

Back

(f∘g)(x) means applying g first and then f, while (g∘f)(x) means applying f first and then g. They are generally not equal.

Front

Given f(x) = 3x + 10 and g(x) = x - 2, find (f∘g)(0).

Back

(f∘g)(0) = f(g(0)) = f(-2) = 4.

Front

Given f(x) = 3x² - 2x + 1 and g(x) = x - 4, find (f*g)(x).

Back

(f*g)(x) = 3x³ - 14x² + 9x - 4.

Front

Given f(x) = -3x + 7 and g(x) = 2x² - 8, find g(f(x)).

Back

g(f(x)) = 18x² - 84x + 90.

Front

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

Back

The quotient of two functions is given by (f/g)(x) = f(x) / g(x), provided g(x) ≠ 0.

Front

Given f(x) = x + 3 and g(x) = x - 2, find (g/f)(x).

Back

(g/f)(x) = (x - 2)/(x + 3).

Front

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

Back

The order of operations is crucial because it determines which function is applied first, affecting the final result.