Function Operations and compositions

Front

What is function composition?

Back

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

Front

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

Back

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

Front

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

Back

The formula for subtracting two functions is f(x) - g(x).

Front

If f(x) = x^2 + 1 and g(x) = 2x - 5, what is f(x) - g(x)?

Back

f(x) - g(x) = (x^2 + 1) - (2x - 5) = x^2 - 2x + 6.

Front

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

Back

f(g(x)) = f(x^2 + 3) = 2(x^2 + 3) = 2x^2 + 6.

Front

How do you multiply two functions f(x) and g(x)?

Back

To multiply two functions, you use the formula f(x) * g(x).

Front

If f(x) = 4x + 8 and g(x) = x + 3, what is f(x) * g(x)?

Back

f(x) * g(x) = (4x + 8)(x + 3) = 4x^2 + 20x + 24.

Front

What is the formula for adding two functions f(n) and g(n)?

Back

The formula for adding two functions is f(n) + g(n).

Front

If f(n) = n^2 + 4n and g(n) = -n - 5, what is f(n) + g(n)?

Back

f(n) + g(n) = (n^2 + 4n) + (-n - 5) = n^2 + 3n - 5.

Front

What does it mean for functions to be defined?

Back

A function is defined when it has a specific rule that assigns exactly one output for each input.