Answer to Question #132875 in Calculus for Everlyn

Question

Create a one-to-one function. It is very important that your function is one-to-one because you will find its inverse. You may not use the function y = x as your one-to-one function.
Post a picture of your function's graph to the discussion board.
State the window used to graph your function. Carefully choose your window so that it shows as much of the function as possible. Find the inverse of your function. You must include your work.

Answer 1

A one-to-one function is a function that has answers that do not repeat. Example of a one-to-one function is $f(x) = x^3$ because it produces different answers for every input.

Now finding the inverse of the function;

$f(x) = x^3$ Replace the f(x) with y

$y = x^3$ Interchange the y and x such that

$x = y ^3$ And then solve for y

${\sqrt[3]x} = (\sqrt[3]{y})^3$ power 3 cancels root 3 leaving;

$y = {\sqrt[3]x}$ Now replace y with f^-1 (x)

f^-1 (x) = ${\sqrt[3]x}$ the inverse of the function

Image of the function and its inverse

On the graph, $y={\sqrt[3]x}$ is the inverse i.e. f^-1 (x) $={\sqrt[3]x}$

The windows used to graph the function are;

On the x-axis; the lower and upper bounds are given as follows;

$-2≤x≤4$

On the y-axis, the lower and upper bounds are given as follows;

$-3≤y≤3$