Finding the inverse of f(x) = -1/7x - 14

[aisha]

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?

 

[kreil]

To check an inverse:

$$f(f^{-1}(x))=f^{-1}(f(x))=x$$

 

[mahesh_2961]

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

 

[aisha]

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.

 

[phreak]

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

 

[aisha]

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

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?

 

[phreak]

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

 

[aisha]

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

how come x+14 is not multiplied by -1? and then by -7?

 

[phreak]

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