Inverse Functions

Front

What is the definition of an inverse function?

Back

An inverse function is a function that reverses the effect of the original function. If the function f takes an input x to an output y, then the inverse function f⁻¹ takes y back to x.

Front

What is the notation used for inverse functions?

Back

The notation for an inverse function is f⁻¹(x), where f is the original function.

Front

How do you find the inverse of a function algebraically?

Back

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

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 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

What is the horizontal line test?

Back

The horizontal line test is a method to determine if a function has an inverse. If any horizontal line intersects the graph of the function more than once, the function does not have an inverse.

Front

What is the significance of one-to-one functions in relation to inverses?

Back

Only one-to-one functions have inverses that are also functions. A one-to-one function means that each output is produced by exactly one input.

Front

How do you verify if two functions are inverses of each other?

Back

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

Front

What is the inverse of a linear function?

Back

The inverse of a linear function can be found by swapping x and y in the equation and solving for y, resulting in another linear function.