Composition of Functions

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. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find g(f(x)) if f(x) = 2x and g(x) = 2x^2 - 1?

Back

To find g(f(x)), substitute f(x) into g: g(f(x)) = g(2x) = 2(2x)^2 - 1 = 8x^2 - 1.

Front

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

Back

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

Front

If f(x) = 3x + 10 and g(x) = x - 2, what is f(g(0))?

Back

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

Front

What does (f ⋅ g)(x) represent?

Back

The product of two functions, (f ⋅ g)(x), is defined as f(x) * g(x).

Front

How do you calculate (f + g)(x) if f(x) = 2x^2 and g(x) = 3x?

Back

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

Front

What is the result of (f ⋅ g)(x) if f(x) = 4x + 8 and g(x) = x + 3?

Back

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

Front

What is the identity function?

Back

The identity function is a function that always returns the same value that was used as its input. It is denoted as I(x) = x.

Front

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

Back

f(g(x)) applies g first and then f to the result, while g(f(x)) applies f first and then g to the result.

Front

How do you evaluate the composition of functions step by step?

Back

To evaluate the composition of functions, first evaluate the inner function, then substitute that result into the outer function.