Function Operations & Compositions of Functions

Front

What is the definition of function operations?

Back

Function operations refer to the mathematical processes of 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

If f(x) = x^2 and g(x) = x + 1, what is (f + g)(x)?

Back

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

Front

If f(x) = 2x and g(x) = x^2, what is (f ⋅ g)(x)?

Back

(f ⋅ g)(x) = 2x * x^2 = 2x^3.

Front

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

Back

To find f(g(x)), substitute g(x) into the function f.

Front

Evaluate f(x) = 3x + 5 for f(2).

Back

f(2) = 3(2) + 5 = 6 + 5 = 11.

Front

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

Back

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

Front

If f(x) = x^2 and g(x) = x - 1, find (f ∘ g)(2).

Back

(f ∘ g)(2) = f(g(2)) = f(2 - 1) = f(1) = 1^2 = 1.

Front

What is the definition of the zero of a function?

Back

The zero of a function is the value of x for which f(x) = 0.

Front

If f(x) = x^2 - 4, what are the zeros of the function?

Back

The zeros are x = 2 and x = -2.