Operations of Functions & Composition of Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

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, denoted as (f ∘ g)(x) = f(g(x)).

Front

If p(x) = 3x + 4, what is p(2)?

Back

p(2) = 3(2) + 4 = 10.

Front

If q(x) = 2x², what is q(3)?

Back

q(3) = 2(3)² = 18.

Front

Find q(p(x)) if p(x) = 3x + 4 and q(x) = 2x².

Back

q(p(x)) = q(3x + 4) = 2(3x + 4)² = 18x² + 48x + 32.

Front

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

Back

The sum of two functions is defined as (f + g)(x) = f(x) + g(x).

Front

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

Back

g(f(-10)) = g(-20) = -20 - 2 = -22.

Front

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

Back

The difference of two functions is defined as (f - g)(x) = f(x) - g(x).

Front

If f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

Back

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

Front

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

Back

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