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.