Composite & Inverse Functions

Front

What is a composite function?

Back

A composite function is formed when one function is applied to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

What is the notation for the inverse of a function f(x)?

Back

The notation for the inverse of a function f(x) is f^(-1)(x).

Front

How do you find the inverse of a function algebraically?

Back

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

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 function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Given f(x) = 2x + 3, find f(4).

Back

f(4) = 2(4) + 3 = 11.

Front

What is the inverse function of f(x) = 3x + 10?

Back

The inverse function is f^(-1)(x) = (x - 10)/3.

Front

If f(x) = x^2, what is the inverse function?

Back

The inverse function is f^(-1)(x) = √x (only for x ≥ 0).

Front

Given j(x) = ∛(x-1) and h(x) = x^3 + 1, find j(h(x)).

Back

j(h(x)) = j(x^3 + 1) = ∛((x^3 + 1) - 1) = ∛(x^3) = x.

Front

What is the composition of functions f(x) = 2x and g(x) = x^2 + 3?

Back

f(g(x)) = f(x^2 + 3) = 2(x^2 + 3) = 2x^2 + 6.