composite and inverse functions flashcard

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f^-1(y) takes y as input and produces x as output.

Front

How do you find the inverse of a linear function?

Back

To find the inverse of a linear function f(x) = ax + b, swap x and y, then solve for y. The result will be the inverse function f^-1(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

What is the composition of functions?

Back

The composition of functions, denoted as (f∘g)(x), means applying function g to x and then applying function f to the result of g.

Front

How do you calculate (f∘g)(x)?

Back

To calculate (f∘g)(x), first evaluate g(x), then substitute that result into f. The expression is (f∘g)(x) = f(g(x)).

Front

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

Back

(f∘g)(0) = f(g(0)) = f(-2) = 3(-2) + 10 = 4.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you find f(g(x)) for two functions f and g?

Back

To find f(g(x)), substitute g(x) into the function f. This means you replace every instance of x in f with g(x).

Front

What is the significance of the domain and range in inverse functions?

Back

The domain of the original function becomes the range of the inverse function, and the range of the original function becomes the domain of the inverse function.

Front

What is the graphical representation of inverse functions?

Back

The graph of an inverse function is a reflection of the graph of the original function across the line y = x.