Operations with Functions

Front

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

Back

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

Front

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

Back

(f + g)(x) = 5x^2 + 6x - 1.

Front

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

Back

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

Front

Given f(x) = 4x + 8 and g(x) = x + 3, find f(x) * g(x).

Back

f(x) * g(x) = 4x^2 + 20x + 24.

Front

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

Back

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

Front

Given m(x) = x^2 + 3x - 7 and g(x) = 3x^2 + 5 + 2x, find g(x) - m(x).

Back

g(x) - m(x) = 2x^2 - x + 12.

Front

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

Back

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

Front

If f(x) = 5x - 1 and c(x) = 2x - 8, find p(x) * c(x).

Back

p(x) * c(x) = 10x^2 - 42x + 8.

Front

What is the definition of a function?

Back

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

Front

What does it mean for two functions to be equal?

Back

Two functions f(x) and g(x) are equal if for every x in their domain, f(x) = g(x).