Question

Determine whether or not the function is one to one and, if so, find the inverse. If the function has an inverse, give the domain of the inverse. $$f(x)=x^{5}$$

Name: Problem 4, Chapter 7: Calculus: One Variable
Uploaded: 2021-08-12T23:09:56-08:00
Duration: 1 min 2 s
Channel: Tyler Moulton
Description: Determine whether or not the function is one to one and, if so, find the inverse. If the function has an inverse, give the domain of the inverse. f(x)=x^5

   Determine whether or not the function is one to one and, if so, find the inverse. If the function has an inverse, give the domain of the inverse.
$$f(x)=x^{5}$$

Calculus: One Variable

Garret J. Etgen,… 10th Edition

Chapter 7, Problem 4

Instant Answer

Solved by Expert Tyler Moulton

08/12/2021

Step 1

A function is one-to-one if it passes the horizontal line test, which means that each horizontal line drawn across the graph of the function intersects the function at most once. The function $f(x) = x^{5}$ is a polynomial function of odd degree, which means its Show more…

Show all steps

Thanks for your feedback!

Determine whether or not the function is one to one and, if so, find the inverse. If the function has an inverse, give the domain of the inverse. $$f(x)=x^{5}$$

Play audio

Feedback

Tyler Moulton and 54 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Injective Functions

A function is one-to-one (injective) if no two different elements in the domain map to the same element in the range. This property is essential because only injective functions have inverses; if f(a) = f(b) then a must equal b.

Inverse Function

The inverse function reverses the roles of inputs and outputs of the original function. If a function f is one-to-one, then its inverse, denoted f?¹, satisfies the conditions f(f?¹(x)) = x and f?¹(f(x)) = x, effectively undoing the operation of f.

Domain and Range Relationship

There is an intrinsic link between the domain and range of a function and its inverse: the domain of the inverse function is exactly the range of the original function, while the range of the inverse is the original domain. This concept is important when establishing the values for which the inverse function is defined.

Please give Ace some feedback