Composition and Inverse Functions (2A Review)

Front

What is a composite function?

Back

A composite function is a function that is formed by combining two functions, where the output of one function becomes the input of another. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you denote the composition of functions a and b?

Back

The composition of functions a and b is denoted as a(b(x)) or (a ∘ b)(x).

Front

What is the value of b(5) if b(5) = 24?

Back

The value of b(5) is 24.

Front

How do you find the value of a(5) if a(5) = 13?

Back

The value of a(5) is 13.

Front

What is the result of b(a(5)) if b(a(5)) = 168?

Back

The result of b(a(5)) is 168.

Front

What is the significance of inverse functions in relation to composite functions?

Back

Inverse functions reverse the effect of the original function. If f is a function and f^(-1) is its inverse, then f(f^(-1)(x)) = x and f^(-1)(f(x)) = x.

Front

How do you calculate the composite function b(a(x))?

Back

To calculate b(a(x)), first find the value of a(x), then substitute that value into the function b.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse undo each other. For a function f and its inverse f^(-1), f(f^(-1)(x)) = x.

Front

What is the domain of a composite function?

Back

The domain of a composite function f(g(x)) is the set of all x in the domain of g such that g(x) is in the domain of f.

Front

What is the range of a composite function?

Back

The range of a composite function f(g(x)) is the set of all possible outputs of f(g(x)).