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, swap the x and y in the equation and 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 line of reflection for inverse functions?

Back

The line of reflection for inverse functions is y = x.

Front

If f(x) = 2x + 3, what is f⁻¹(x)?

Back

f⁻¹(x) = (x - 3)/2.

Front

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

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 domain of an inverse function?

Back

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

Front

What is the range of an inverse function?

Back

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

Front

How can you verify if two functions are inverses?

Back

To verify if two functions are inverses, check if f(g(x)) = x and g(f(x)) = x.

Front

What is the notation for an inverse function?

Back

The notation for an inverse function is f⁻¹(x).