Finding Inverses of Functions

Front

What is 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 and produces x.

Front

How do you find the inverse of a function algebraically?

Back

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

Front

What is the notation for the inverse of a function g(x)?

Back

The inverse of g(x) is denoted as g⁻¹(x).

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse are reflections of each other across the line y = x.

Front

What does it mean for two functions to be inverses?

Back

Two functions f and g are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

What is the inverse of the coordinates (1, 2)?

Back

The inverse of the coordinates (1, 2) is (2, 1).

Front

What is the inverse of the function f(x) = 3x + 2?

Back

To find the inverse, swap x and y: x = 3y + 2, then solve for y: f⁻¹(x) = (x - 2)/3.

Front

What is the graphical representation of a function and its inverse?

Back

The graph of a function and its inverse are symmetric with respect to the line y = x.

Front

What is the domain of a function's inverse?

Back

The domain of the inverse function is the range of the original function.

Front

What is the range of a function's inverse?

Back

The range of the inverse function is the domain of the original function.