Week 13 (PT): Inverse Relation and Inverse Function

Front

What is an inverse relation?

Back

An inverse relation is a relation that reverses the input and output of a function. If a function is represented as (x, y), its inverse will be represented as (y, x).

Front

What is an inverse function?

Back

An inverse function is a function that 'undoes' the action of the original function. If f(x) is a function, then its inverse f^{-1}(x) satisfies the equation f(f^{-1}(x)) = x.

Front

How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test on a graph.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If any vertical line intersects the curve at more than one point, the curve is not a function.

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. This means that for every y-value, there is exactly one x-value.

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 function f(x) = 2x + 4?

Back

The inverse is f^{-1}(x) = \frac{x - 4}{2}.

Front

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

Back

The inverse is f^{-1}(x) = -\frac{1}{4}x - 3.

Front

What is the range of an inverse function?

Back

The range of an inverse function is the same as the domain of the original function.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.