Inverses and Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions 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

How do you find the inverse of a function?

Back

To find the inverse of a function f(x), you swap the x and y in the equation and solve for y. The inverse is denoted as f^(-1)(x).

Front

What is the inverse of f(x) = 3x + 2?

Back

f^(-1)(x) = (x - 2) / 3.

Front

What is the composition f(g(x)) if f(x) = 5x and g(x) = 2x - 1?

Back

f(g(x)) = 10x - 5.

Front

What is the composition g(f(x)) if f(x) = x - 1 and g(x) = 2x?

Back

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

Front

What is the inverse of f(x) = x^3 - 1?

Back

f^(-1)(x) = ∛(x + 1).

Front

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

Back

(f ° f)(-2) = 97.

Front

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

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

How do you verify if two functions are inverses?

Back

To verify if f(x) and g(x) are inverses, check if f(g(x)) = x and g(f(x)) = x.

Front

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

Back

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