Function Operations & Compositions of Functions

Front

What are function operations?

Back

Function operations involve combining two or more functions using addition, subtraction, multiplication, or division.

Front

What is function composition?

Back

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

Front

How do you determine if two functions are inverses?

Back

Two functions f(x) and g(x) are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

What is the formula for the product of two functions?

Back

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

Front

How do you find (f + g)(x) for two functions?

Back

To find (f + g)(x), add the outputs of the two functions: (f + g)(x) = f(x) + g(x).

Front

Evaluate f(x) = 3x^2 - 2x + 1 for f(2).

Back

f(2) = 3(2)^2 - 2(2) + 1 = 3(4) - 4 + 1 = 12 - 4 + 1 = 9.

Front

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

Back

(f ⋅ g)(x) = f(x) * g(x) = 2x * (x + 3) = 2x^2 + 6x.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the value of the variable into the function's expression.

Front

What is the sum of f(x) = x^2 and g(x) = 2x + 1?

Back

(f + g)(x) = f(x) + g(x) = x^2 + (2x + 1) = x^2 + 2x + 1.

Front

What is the difference of two functions?

Back

The difference of two functions f(x) and g(x) is given by (f - g)(x) = f(x) - g(x).