Operation and Composition of Functions

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from a set of inputs.

Front

What does it mean to compose functions?

Back

Composing functions means applying one function to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

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

Back

To find (g + f)(x), you add the outputs of g(x) and f(x) for the same input x.

Front

What is the order of operations when evaluating f(g(x))?

Back

The order is INSIDE then OUT, meaning you evaluate g(x) first, then apply f to that result.

Front

If f(x) = x^2 - 3, what is f(3)?

Back

f(3) = 3^2 - 3 = 9 - 3 = 6.

Front

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

Back

f(g(f(3))) = f(g(6)) = f(3) = 6.

Front

What is the definition of the sum of functions?

Back

The sum of functions, (f + g)(x), is defined as f(x) + g(x) for all x in the domain.

Front

How do you evaluate -2f(x) if f(x) = 3x^2 + 4?

Back

-2f(x) = -2(3x^2 + 4) = -6x^2 - 8.

Front

What is the output of f(x) = 3x^2 + 4 when x = -2?

Back

f(-2) = 3(-2)^2 + 4 = 3(4) + 4 = 12 + 4 = 16.

Front

What is the definition of the difference of functions?

Back

The difference of functions, (f - g)(x), is defined as f(x) - g(x) for all x in the domain.