Operations With Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as f(x), where x is the input.

Front

Evaluate f(-2) if f(x) = x + 3.

Back

f(-2) = -2 + 3 = 1.

Front

What does (f + g)(x) represent?

Back

It represents the sum of two functions f(x) and g(x), calculated as (f + g)(x) = f(x) + g(x).

Front

Evaluate (g + f)(-3) if g(x) = -2x + 2 and f(x) = 3x^2 + 4.

Back

(g + f)(-3) = g(-3) + f(-3) = 8 + 31 = 39.

Front

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

Back

f(x) and g(x) are two different functions that can be combined through addition, subtraction, multiplication, or division.

Front

Evaluate f(n) + g(n) if f(n) = 2n + 1 and g(n) = 3n.

Back

f(n) + g(n) = (2n + 1) + (3n) = 5n + 1.

Front

What is the product of two functions f(x) and g(x)?

Back

The product is denoted as (f * g)(x) = f(x) * g(x).

Front

Evaluate f(x) * g(x) if f(x) = 3 and g(x) = -2x + 5.

Back

f(x) * g(x) = 3 * (-2x + 5) = -6x + 15.

Front

What is the composition of functions?

Back

The composition of functions f and g is denoted as (f ∘ g)(x) = f(g(x)).

Front

Evaluate (f * g)(1) if f(x) = 2x and g(x) = x + 3.

Back

(f * g)(1) = f(1) * g(1) = 2 * (1 + 3) = 8.