Unit 6 Test Review - Compositions and Inverses

Front

What is the composition of two functions f(x) and g(x)?

Back

The composition of two functions f(x) and g(x) is denoted as f(g(x)), which means you apply g first and then apply f to the result.

Front

How do you find f(g(5)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

First, calculate g(5): g(5) = 5 - 2 = 3. Then, calculate f(g(5)): f(3) = 3(3) + 10 = 19.

Front

What is the value of f(g(3)) if f(x) = 2x and g(x) = 2x^2 - 1?

Back

First, calculate g(3): g(3) = 2(3^2) - 1 = 18 - 1 = 17. Then, calculate f(g(3)): f(17) = 2(17) = 34.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements, meaning each output is unique to its input.

Front

What line is the inverse of a function reflected over?

Back

The inverse of a function is reflected over the line y = x.

Front

How do you determine if a function is one-to-one from its graph?

Back

A function is one-to-one if any horizontal line intersects the graph at most once.

Front

What is the process to find the inverse of a function?

Back

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

Front

What is the significance of function composition in mathematics?

Back

Function composition allows us to combine two functions into a single function, enabling more complex operations and transformations.

Front

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

Back

The inverse function is f^(-1)(x) = √x, but it is only valid for x ≥ 0 to ensure it is one-to-one.

Front

What is the output of f(g(2)) if f and g are defined on a graph?

Back

To find f(g(2)), locate g(2) on the graph, then find the corresponding output of f at that value.