Operations & Composition Functions

Front

Define function composition.

Back

Function composition is the process of applying one function to the results of another function. If f(x) and g(x) are two functions, the composition is denoted as (f ∘ g)(x) = f(g(x)).

Front

What is the formula for adding two functions f(x) and g(x)?

Back

The sum of two functions is given by (f + g)(x) = f(x) + g(x).

Front

How do you find the product of two functions f(x) and g(x)?

Back

The product of two functions is given by (f * g)(x) = f(x) * g(x).

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Given f(x) = 2x + 3, find f(2).

Back

f(2) = 2(2) + 3 = 7.

Front

Given g(x) = x^2, find g(-3).

Back

g(-3) = (-3)^2 = 9.

Front

If f(x) = x + 1 and g(x) = 2x, find (f ∘ g)(3).

Back

(f ∘ g)(3) = f(g(3)) = f(2(3)) = f(6) = 6 + 1 = 7.

Front

What is the formula for finding the quotient of two functions f(x) and g(x)?

Back

The quotient of two functions is given by (f / g)(x) = f(x) / g(x), with g(x) ≠ 0.

Front

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

Back

(f * g)(x) = f(x) * g(x) = 3x^2(x - 1) = 3x^3 - 3x^2.