+0  
 
0
69
1
avatar+36 

The function f(x) is invertible, but the function g(x)=f(kx)  is not invertible. Find the sum of all possible values of k.

grif389  Oct 6, 2018

Best Answer 

 #1
avatar+3231 
+1

\(\text{Assuming }f(x) \text{ is invertible }\forall x \in \mathbb{R} \\ \text{then }\forall k\neq 0, \exists y = k x \ni f^{-1}(y) = k x \\ \text{i.e. }f(kx) \text{ is invertible.}\\ \text{Thus it must be the only value of k that makes the original statement is valid is }\\ k=0 \\ \text{and the sum of this is just 0} \\ \text{It's true that }\exists f(0) \ni f^{-1}(f(0))=0 \text{ but }f(0\cdot x) \text{ is not invertible}\)

Rom  Oct 6, 2018
 #1
avatar+3231 
+1
Best Answer

\(\text{Assuming }f(x) \text{ is invertible }\forall x \in \mathbb{R} \\ \text{then }\forall k\neq 0, \exists y = k x \ni f^{-1}(y) = k x \\ \text{i.e. }f(kx) \text{ is invertible.}\\ \text{Thus it must be the only value of k that makes the original statement is valid is }\\ k=0 \\ \text{and the sum of this is just 0} \\ \text{It's true that }\exists f(0) \ni f^{-1}(f(0))=0 \text{ but }f(0\cdot x) \text{ is not invertible}\)

Rom  Oct 6, 2018

12 Online Users

avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.