Composition of Functions Flashcard

Front

What is the composition of functions?

Back

The composition of functions is a process where one function is applied to the result of another function. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

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

Back

(f ∘ g)(2) = f(g(2)) = f(3(2) + 2) = f(8) = 2(8) = 16.

Front

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

Back

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

Front

If f(x) = 2x + 3 and g(x) = -3x - 4, what is f(x) ⋅ g(x)?

Back

f(x) ⋅ g(x) = (2x + 3)(-3x - 4) = -6x^2 - 17x - 12.

Front

What does f(g(x)) represent?

Back

f(g(x)) represents the composition of f and g, where g is applied first and then f is applied to the result.

Front

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

Back

f(g(x)) = f(2x^2 - 1) = 2(2x^2 - 1) = 4x^2 - 2.

Front

What is the value of g(f(2)) if f(x) = 2x and g(x) = 2x^2 - 1?

Back

g(f(2)) = g(2(2)) = g(4) = 2(4^2) - 1 = 32 - 1 = 31.

Front

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

Back

g(f(x)) = g(2x) = 2(2x)^2 - 1 = 8x^2 - 1.

Front

What is the identity function?

Back

The identity function is a function that always returns the same value that was used as its input. It is denoted as I(x) = x.

Front

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

Back

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