Register to reply

Question regarding inverse functions

by michellemich
Tags: functions, inverse
Share this thread:
michellemich
#1
Aug22-13, 12:09 PM
P: 1
f(x) where x belongs to all real numbers
inverse: f-1(x), where x belongs to all real numbers

True or False:
The inverse of f(x+3) is f-1(x+3)

My ideas:
I think that it is false given that when you usually find the inverse of a function, you switch the x and y variables and solve for y again meaning that the inverse couldn't stay the same.
I figured since the domain and range of f(x) belong to all real numbers, possibly f(x) = x and then inputting f(x+3) = x+ 3
then y = x+3
then y = x - 3 but im not really sure if thats right :s
Phys.Org News Partner Mathematics news on Phys.org
'Moral victories' might spare you from losing again
Fair cake cutting gets its own algorithm
Effort to model Facebook yields key to famous math problem (and a prize)
LCKurtz
#2
Aug22-13, 01:49 PM
HW Helper
Thanks
PF Gold
LCKurtz's Avatar
P: 7,566
Quote Quote by michellemich View Post
f(x) where x belongs to all real numbers
inverse: f-1(x), where x belongs to all real numbers

True or False:
The inverse of f(x+3) is f-1(x+3)

My ideas:
I think that it is false given that when you usually find the inverse of a function, you switch the x and y variables and solve for y again meaning that the inverse couldn't stay the same.
I figured since the domain and range of f(x) belong to all real numbers, possibly f(x) = x and then inputting f(x+3) = x+ 3
then y = x+3
then y = x - 3 but im not really sure if thats right :s
You are given that ##f## has an inverse ##f^{-1}##. What happens when you solve the equation ##y=f(x+3)## for ##x##?
BrettJimison
#3
Aug22-13, 04:14 PM
P: 37
Good Day michellemich!

If you are not sure of your answer, try some composition: let your original function be f(x)and your questionable inverse function be g(x)

Evaluate (f of g) and (g of f). If they undo each other, they are inverses.

HallsofIvy
#4
Aug22-13, 06:26 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,318
Question regarding inverse functions

If you want to know if this is true for all invertible functions, it is simple enough to find a counterexample.

If, say, f(x)= 2x+ 3, then [itex]f(x)= 3x- 2[/itex], then [itex]f^{-1}(x)= (x+ 2)/3[/itex]. f(x+3)= 3(x+ 3)- 2= 3x+ 7. The inverse of that function is [itex](x- 7)/3[/itex]. Is that equal to [itex]f^{-1}(x+ 3)= (x+3+ 2)/3= (x+ 5)/3[/itex]?


Register to reply

Related Discussions
Question on Jacobian with function composition and inverse functions General Math 7
A question regarding inverse functions Precalculus Mathematics Homework 15
A question about restrictions of inverse functions Precalculus Mathematics Homework 2
Question about integration with inverse trigonometric functions Calculus & Beyond Homework 1
Question about inverse functions Precalculus Mathematics Homework 2