Flashcardizz Compostiotion of Functions

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

What does it mean for two functions to be inverses of each other?

Back

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

Front

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

Back

(f ∘ g)(x) = f(g(x)) = f(3x + 2) = 2(3x + 2) = 6x + 4.

Front

What is the formula for finding the inverse of a function?

Back

To find the inverse of a function f(x), swap x and y in the equation y = f(x) and solve for y.

Front

If f(x) = 1/x, what is the inverse function f^{-1}(x)?

Back

The inverse function f^{-1}(x) = 1/x.

Front

What is the result of f(g(x)) if f(x) = 1/x and g(x) = 3x + 2?

Back

f(g(x)) = f(3x + 2) = 1/(3x + 2).

Front

How do you find (g ∘ f)(x) for f(x) = 1/x and g(x) = 3x + 2?

Back

(g ∘ f)(x) = g(f(x)) = g(1/x) = 3(1/x) + 2 = 3/x + 2.

Front

What is the composition of f(x) = (8x - 3)/5 and its inverse?

Back

The composition f(f^{-1}(x)) = x for all x in the domain.

Front

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

Back

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

Front

What is the significance of the identity function in function composition?

Back

The identity function, I(x) = x, serves as a neutral element in function composition, meaning f(I(x)) = f(x) and I(f(x)) = f(x).