- #1
aisha
- 584
- 0
f(x)=-1/7x-14 is the inverse of this f^-1(x)=[7(x+14)]/(-1) ? Can someone please check for me if not what did I do wrong? 
Check Inverse f(x)=-1/7x-14: Right or Wrong?
- Thread starter aisha
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Homework Help Overview
The discussion revolves around verifying the inverse of the function f(x) = -1/7x - 14. Participants are examining the correctness of the proposed inverse function and the methods used to derive it.
Discussion Character
- Conceptual clarification, Mathematical reasoning, Assumption checking
Approaches and Questions Raised
- Participants explore the definition of an inverse function and check the validity of the proposed inverse by applying the condition f(f^{-1}(x)) = f^{-1}(f(x)) = x. There are attempts to manipulate the original function to derive the inverse, with some questioning the correctness of specific steps and simplifications.
Discussion Status
Some participants provide guidance on checking the inverse and suggest methods for simplification. There is an ongoing exploration of different approaches to arrive at the inverse, with no explicit consensus on the final form of the inverse function.
Contextual Notes
Participants express uncertainty about the correctness of their methods and results, particularly regarding the handling of negative signs and simplifications. There is a focus on ensuring that the inverse function is accurately derived from the original function.
- #2
kreil
Science Advisor
- 665
- 68
To check an inverse:
[tex]f(f^{-1}(x))=f^{-1}(f(x))=x[/tex]
[tex]f(f^{-1}(x))=f^{-1}(f(x))=x[/tex]
- #3
mahesh_2961
- 20
- 0
Its very easy ..
put y = -1/(7x-14)
and solve for x
u will get
x= (14y-1)/7y
so the inverse function of f(x) is f-1(x) = (14x-1)/7x
put y = -1/(7x-14)
and solve for x
u will get
x= (14y-1)/7y
so the inverse function of f(x) is f-1(x) = (14x-1)/7x
- #4
aisha
- 584
- 0
The question is (-1/7)x-14 is my answer incorrect? f^-1(x)=[7(x+14)]/-1?
I don't know if the -1 is right and not sure about the answer either.
I don't know if the -1 is right and not sure about the answer either.
- #5
phreak
- 133
- 1
The -1 is correct and your answer is correct... I don't know how you got around to dividing by -1 as you must have used a different method, but it's correct nonetheless.
If you want to check these problems by yourself in the future, an easy way is to graph both functions. They should reflect over the function f(x) = x
If you want to check these problems by yourself in the future, an easy way is to graph both functions. They should reflect over the function f(x) = x
Last edited:
- #6
aisha
- 584
- 0
phreak said:
This is what I did. x=(-1/7)y-14
x+14=(-1/7)y
7(x+14)=-1y
divide both sides by -1 and get
[7(x+14)]/-1 but can this be simplified? Can I get rid of the -1 somehow or is the correct way of writing it?
- #7
phreak
- 133
- 1
Yes, dividing by -1 is basically the same as multiplying by -1 (in this situation). Make everything negative.
[7(x+14)]/-1 yields:
-7(x+14)
which, simplified is:
-7x-98
[7(x+14)]/-1 yields:
-7(x+14)
which, simplified is:
-7x-98
- #8
aisha
- 584
- 0
phreak said:
how come x+14 is not multiplied by -1? and then by -7?
- #9
phreak
- 133
- 1
Well, it's easier if you simplify first.
[7(x+14)]/-1 can be simplified by multiplying 7(x+14).
7(x+14) = (7x + 98) and now you can divide by -1
(7x + 98)/-1 is the same thing as (7x/-1) + (98/-1) which brings the final result to:
-7x - 98
[7(x+14)]/-1 can be simplified by multiplying 7(x+14).
7(x+14) = (7x + 98) and now you can divide by -1
(7x + 98)/-1 is the same thing as (7x/-1) + (98/-1) which brings the final result to:
-7x - 98