how do i verify an inverse of a function?

[Failenn]

I have to find the inverse of f(x) = 3x + 7 and then verify f & f-1 are inverses algebraically.

This is how I did it...

f(x) = 3x + 7
y = 3x + 7
x = 3y + 7
x - 7 = 3y
x - 7 = y
3


to do the inverse I solved this way...
f-1(x) = x - 7
3
y = x - 7
3
x = y - 7
3
3x = y - 7
3x + 7 = y

I'm missing something but not sure what. Thanks for the help.

 

[Failenn]

I have answered my own question. I went back and for the inverse I substitued my y value that I found in the first problem and solved it to make x = x.

 

[Deleted member 4993]

I have to find the inverse of f(x) = 3x + 7 and then verify f & f-1 are inverses algebraically.

This is how I did it...

f(x) = 3x + 7
y = 3x + 7
x = 3y + 7 ? You switched "x" and "y"
x - 7 = 3y
x - 7 = y ? This is the inverse = f[sup:36hw7gzt]-1[/sup:36hw7gzt](x) = g(x)
3
To check you should find the following:

f[sup:36hw7gzt]-1[/sup:36hw7gzt][f(x)] = [f(x) - 7]/3 = [(3x+7)-7]/3 = 3x/3 = x ? checks

 

[Failenn]

thanks. I see what you did and it makes much more sense.