Inverse of Function

Front

What is the definition of the inverse of a function?

Back

The inverse of a function f(x) is a function that reverses the effect of f. If f takes an input x to an output y, then the inverse function f^-1 takes y back to x.

Front

If f(1) = 4, what is f^-1(4)?

Back

f^-1(4) = 1.

Front

What is the relationship between the points on a function and its inverse?

Back

The points (a, b) on the function f correspond to the points (b, a) on its inverse f^-1.

Front

How do you find the inverse of a function algebraically?

Back

1. Replace f(x) with y. 2. Switch 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 + 3?

Back

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

Front

True or False: The inverse of a function is also a function.

Back

True, as long as the original function is one-to-one.

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.

Front

If f(x) has the points (2, 5) and (3, 7), what points are on f^-1(x)?

Back

(5, 2) and (7, 3).

Front

What is the graphical representation of a function and its inverse?

Back

The graph of a function and its inverse are symmetric with respect to the line y = x.

Front

If f(0) = 3, what can you say about f^-1(3)?

Back

f^-1(3) = 0.