Module 5 Practice Test

Front

What is the composition of functions?

Back

The composition of functions is a way to combine two functions where the output of one function becomes the input of another. It is denoted as (g ∘ f)(x) = g(f(x)).

Front

How do you find the inverse of a function?

Back

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

Front

What is the significance of the inverse function?

Back

The inverse function undoes the action of the original function. If f(x) takes x to y, then f^{-1}(y) takes y back to x.

Front

What does f^{-1}(3) represent?

Back

f^{-1}(3) represents the value of x such that f(x) = 3. It is the x-coordinate of the point on the graph where the output is 3.

Front

How do you interpret the graph of a function to find its inverse?

Back

To find the inverse from a graph, reflect the graph over the line y = x. The new graph represents the inverse function.

Front

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

Back

For a linear function f(x) = mx + b, the inverse is f^{-1}(x) = (x - b)/m.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse are symmetric with respect to the line y = x. This means that if (a, b) is on the graph of f, then (b, a) is on the graph of f^{-1}.

Front

What is the domain and range of a function and its inverse?

Back

The domain of a function f is the range of its inverse f^{-1}, and the range of f is the domain of f^{-1}.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function f at a specific point x, substitute x into the function's equation and simplify.

Front

What is the process for solving for x in a linear equation?

Back

To solve for x in a linear equation, isolate x on one side of the equation using algebraic operations such as addition, subtraction, multiplication, or division.