SOLUTION: what is the inverse of f(x)=10/5x+2? and what is the domain and rage for both f(x) and f^-1(x)?

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Question 1092562: what is the inverse of f(x)=10/5x+2?
and what is the domain and rage for both f(x) and f^-1(x)?
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!

One version of the standard way to find the inverse of a function is to switch the x and y in the given function and solve for the new y.

x+=+10%2F5y+%2B+2
x-2+=+2%2Fy
y+=+2%2F%28x-2%29

In the given function, 0 is excluded from the domain because it would make the denominator 0. That means 0 is excluded from the range of the inverse function.

You can also see that 0 is not in the range of the inverse function, because if you try to solve
2%2F%28x-2%29+=+0
you get no solution.

Similarly you can see that 2 is excluded from the range of the given function, because, again, if you try to solve
10%2F5y+%2B+2+=+2
you will get no solution. And since 2 is excluded from the range of the given function, it is excluded from the domain of the inverse function. And we can see that by looking at the inverse function, because x=2 would make the denominator 0.

In summary...

For the given function,
Domain is x not equal to 0
Range is y not equal to 2

For the inverse function,
Domain is x not equal to 2
Range is y not equal to 0