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 notation for an inverse function?

Back

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

Front

If f(x) = 2x + 3, what is f^-1(x)?

Back

f^-1(x) = (x - 3)/2.

Front

What is the relationship between a function and its inverse?

Back

If f is a function and f^-1 is its inverse, then f(f^-1(x)) = x and f^-1(f(x)) = x for all x in the domain.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements, ensuring that it has an inverse.

Front

How can you determine if a function has an inverse?

Back

A function has an inverse if it is one-to-one, which can be tested using the horizontal line test.

Front

What is the inverse of the function f(x) = 1/4x - 7?

Back

f^-1(x) = 4x + 28.

Front

What is the inverse of the points (1,3)(2,4)(6,2)?

Back

The inverse points are (3,1)(4,2)(2,6).