Inverse 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 back to x.

Front

How do you find the inverse of a function algebraically?

Back

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

Front

What is the graphical representation of an inverse function?

Back

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

Front

What is the first step in finding the inverse of f(x) = 2x - 2?

Back

Switch x and y: x = 2y - 2.

Front

What is the inverse of f(x) = 2x - 2?

Back

f⁻¹(x) = 1/2x + 1.

Front

What does it mean if two functions are inverses of each other?

Back

If f(g(x)) = x and g(f(x)) = x for all x in the domain, then f and g are inverse functions.

Front

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

Back

The line y = x serves as the line of reflection for the graphs of a function and its inverse.

Front

Can a function have more than one inverse?

Back

No, a function can have at most one inverse unless it is not a one-to-one function.

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

How can you verify if two functions are inverses?

Back

To verify, check if f(g(x)) = x and g(f(x)) = x for all x in the domain.