Finding Inverse Equations Practice

Front

What is an inverse function?

Back

An inverse function is a function that reverses the effect of the original function. If the function f takes an input x to an output y, then the inverse function f⁻¹ takes y back to x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse of a function algebraically, follow these steps: 1) Replace f(x) with y. 2) Swap x and y. 3) Solve for y. 4) Replace y with f⁻¹(x).

Front

What is the relationship between a function and its inverse?

Back

The relationship is that if (a, b) is a point on the function f, then (b, a) is a point on its inverse f⁻¹. This means that the graphs of a function and its inverse are reflections of each other across the line y = x.

Front

What is the horizontal line test and how does it relate to inverse functions?

Back

The horizontal line test is a method to determine if a function has an inverse. If any horizontal line intersects the graph of the function more than once, the function does not have an inverse.

Front

What is the domain and range of a function and its inverse?

Back

The domain of a function is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values). For the inverse function, the domain and range are swapped.

Front

How do you verify if two functions are inverses of each other?

Back

To verify if two functions f and g are inverses, check if f(g(x)) = x and g(f(x)) = x for all x in the domain of f and g.

Front

What is the significance of the notation f⁻¹(x)?

Back

The notation f⁻¹(x) represents the inverse function of f(x). It is important to note that this does not mean '1 divided by f'.

Front

Can a function have more than one inverse?

Back

No, a function can have at most one inverse. If a function is not one-to-one (does not pass the horizontal line test), it cannot have an inverse.

Front

What is the process of graphing the inverse of a function?

Back

To graph the inverse of a function, reflect the graph of the original function across the line y = x.

Front

What are some common types of functions that have inverses?

Back

Common types of functions that have inverses include linear functions, quadratic functions (restricted to one side of the vertex), exponential functions, and logarithmic functions.