Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the effect 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 back to x.

Front

How is the inverse of a function denoted?

Back

The inverse of a function f(x) is denoted as f^-1(x).

Front

What does it mean for two functions to be inverses of each other?

Back

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

Front

What is the graphical representation of inverse functions?

Back

Inverse functions are reflected over the line y = x in a coordinate plane.

Front

What is the relationship between the domains and ranges of a function and its inverse?

Back

The domain of f(x) becomes the range of f^-1(x), and the range of f(x) becomes the domain of f^-1(x).

Front

What is the first step to find the inverse of a function algebraically?

Back

To find the inverse of a function, first replace f(x) with y.

Front

How do you solve for the inverse function after replacing f(x) with y?

Back

Swap x and y in the equation and then solve for y to find the inverse function.

Front

What is the significance of the line y = x in relation to inverse functions?

Back

The line y = x serves as a mirror line; points on the graph of a function and its inverse are symmetric with respect to this line.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input, ensuring that it has an inverse.

Front

Can all functions have inverses?

Back

Not all functions have inverses; only one-to-one functions have inverses that are also functions.