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

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

Back

(f + g)(x) represents the sum of two functions f(x) and g(x). It is calculated by adding the outputs of f and g for the same input x.

Front

How do you find (g + f)(-3) if g(x) = -2x + 2 and f(x) = 3x² + 4?

Back

First, calculate g(-3) = -2(-3) + 2 = 8. Then, calculate f(-3) = 3(-3)² + 4 = 27. Finally, (g + f)(-3) = 8 + 27 = 35.

Front

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

Back

(f - g)(x) = f(x) - g(x). It represents the difference between the outputs of f and g for the same input x.

Front

If f(x) = 3x² + 7x and g(x) = 2x² - x - 1, what is (f + g)(x)?

Back

(f + g)(x) = (3x² + 7x) + (2x² - x - 1) = 5x² + 6x - 1.

Front

What does (f * g)(x) mean?

Back

(f * g)(x) represents the product of two functions f(x) and g(x). It is calculated by multiplying the outputs of f and g for the same input x.

Front

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

Back

f(n) * g(n) = (2n + 1) * (3n) = 6n² + 3n.

Front

What is the result of (f - g)(x) if f(x) = 3x² and g(x) = 2x² + 3x?

Back

(f - g)(x) = 3x² - (2x² + 3x) = x² - 3x.

Front

Define the term 'composite function'.

Back

A composite function is formed when one function is applied to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

What is the output of (f + g)(2) if f(x) = x² and g(x) = 2x?

Back

(f + g)(2) = f(2) + g(2) = 2² + 2(2) = 4 + 4 = 8.