Composite & Inverse Functions

Front

What is a composite function?

Back

A composite function is a function that is formed by combining two functions, denoted as (f∘g)(x) = f(g(x)).

Front

What is the inverse function of a quadratic (x²)?

Back

A square root function.

Front

What are the steps to find the inverse of a function?

Back

1. Replace f(x) with y. 2. Switch x and y. 3. Solve for y. 4. Replace y with f⁻¹(x).

Front

If f(x) = 3x + 10, what is f(0)?

Back

f(0) = 10.

Front

If g(x) = x - 2, what is g(0)?

Back

g(0) = -2.

Front

What is (f∘g)(0) if f(x) = 3x + 10 and g(x) = x - 2?

Back

(f∘g)(0) = 4.

Front

Are the functions f(x) = 2x and g(x) = x/2 inverses of each other?

Back

True.

Front

What is the inverse of f(x) = -4x - 12?

Back

f⁻¹(x) = -1/4x - 3.

Front

What is the domain of the square root function?

Back

The domain is x ≥ 0.

Front

What is the range of the function f(x) = x²?

Back

The range is y ≥ 0.