Inverse of Function

Front

What is 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, denoted as f^(-1)(y), takes y back to x.

Front

If the point (a, b) is on the function f(x), what point is on the inverse f^(-1)(x)?

Back

The point (b, a) is on the inverse function f^(-1)(x).

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 first step in finding the inverse of f(x) = 3x + 5?

Back

Replace f(x) with y: y = 3x + 5.

Front

What is the inverse of the function f(x) = 2x - 4?

Back

The inverse is f^(-1)(x) = (x + 4)/2.

Front

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

Back

True, but only if the original function is one-to-one (bijective).

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) = x^2, what is the inverse?

Back

f(x) = x^2 is not one-to-one, so it does not have an inverse unless restricted to x >= 0.

Front

What is the relationship between the graphs of a function and its inverse?

Back

The graphs of a function and its inverse are reflections of each other across the line y = x.

Front

What is the inverse of f(x) = 1/x?

Back

The inverse is f^(-1)(x) = 1/x.