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 as input and produces x as output.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse of a function algebraically, follow these steps: 1. Replace f(x) with y. 2. Swap x and y. 3. Solve for y. 4. Replace y with f^-1(x).

Front

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

Back

The inverse of the function f(x) = 2x - 2 is f^-1(x) = 1/2x + 1.

Front

What is the inverse of the function f(x) = -4x - 12?

Back

The inverse of the function f(x) = -4x - 12 is f^-1(x) = -1/4x - 3.

Front

What is the significance of the notation f^-1(x)?

Back

The notation f^-1(x) represents the inverse function of f(x). It is not the same as raising f to the power of -1.

Front

What is the graphical representation of inverse functions?

Back

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

Front

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

Back

The domain of a function is the range of its inverse, and the range of a function is the domain of its inverse.

Front

How can 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 the function f(x) = 1/4x - 7?

Back

The inverse of the function f(x) = 1/4x - 7 is f^-1(x) = 4x + 28.

Front

What is the importance of finding inverse functions in real-world applications?

Back

Finding inverse functions is important in real-world applications as it allows us to determine original values from transformed data, such as in finance, physics, and engineering.