My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
January 19th, 2014, 07:33 PM   #1
Newbie
 
Joined: Jan 2014

Posts: 19
Thanks: 0

Invertible Functions

Determine whether f(x) = x^4 + 3x^3 +1 is invertible.

f'(x) = 4x^3 + 9x^2

... I'm not sure what to do next, or if that's even the way to begin solving. I'd really appreciate some help with this problem.
ceity is offline  
 
January 19th, 2014, 09:49 PM   #2
Math Team
 
agentredlum's Avatar
 
Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,372
Thanks: 233

Re: Invertible Functions

f(0) = 1

f(-3) = 1

So , we have two distinct values of x that produce the same value of y , therefore the function is not invertible. In other words , the point's (0 , 1) , (-3 , 1) are both on the graph so it definitely fails the horizontal line test there.

Alternatively , any polynomial that has a positive even power of x will not be invertible. For this polynomial , the x^4 term makes it non-invertible

agentredlum is offline  
January 20th, 2014, 02:08 AM   #3
Newbie
 
Joined: Jan 2014

Posts: 19
Thanks: 0

Re: Invertible Functions

Quote:
Originally Posted by agentredlum
f(0) = 1

f(-3) = 1

So , we have two distinct values of x that produce the same value of y , therefore the function is not invertible. In other words , the point's (0 , 1) , (-3 , 1) are both on the graph so it definitely fails the horizontal line test there.

Alternatively , any polynomial that has a positive even power of x will not be invertible. For this polynomial , the x^4 term makes it non-invertible

Got it. Thank you very much.
ceity is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
functions, invertible



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Why Isn't This Matrix Invertible? Magnesium Linear Algebra 2 December 11th, 2013 02:09 AM
Transformation is not invertible soumita Linear Algebra 3 April 28th, 2013 04:49 PM
invertible matrix shine123 Linear Algebra 1 September 21st, 2012 08:47 AM
T: V to V and [T]_B is invertible tinynerdi Linear Algebra 0 February 20th, 2010 05:58 PM
Show that A must be invertible 450081592 Linear Algebra 1 November 28th, 2009 01:32 AM





Copyright © 2019 My Math Forum. All rights reserved.