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, replace f(x) with y, swap x and y, and then solve for y. The resulting equation is the inverse function.

Front

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

Back

The inverse of the points is (3,1)(4,2)(2,6).

Front

Find the inverse of the function f(x) = 1/4x - 7.

Back

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

Front

What is the inverse of g(x) = -7x^5 + 7?

Back

The inverse is g^-1(x) = -^5\sqrt{\frac{x-7}{7}}.

Front

How do you graph a function and its inverse?

Back

To graph a function and its inverse, plot both on the same coordinate plane. The graph of the inverse is a reflection of the original function across the line y = x.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse are symmetric with respect to the line y = x.

Front

What is the inverse of f(x) = 5x + 1?

Back

The inverse is f^-1(x) = \frac{x-1}{5}.

Front

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

Back

A function is one-to-one if it passes the horizontal line test, meaning no horizontal line intersects the graph more than once.

Front

What is the horizontal line test?

Back

The horizontal line test determines if a function is one-to-one. If any horizontal line intersects the graph more than once, the function does not have an inverse.