SOLUTION: I need help with this problem: Show that the function f(x)=1/(x-2) is one-to-one via cketching its graph. Then find its inverse function. Thank you very much.

Algebra ->  Functions -> SOLUTION: I need help with this problem: Show that the function f(x)=1/(x-2) is one-to-one via cketching its graph. Then find its inverse function. Thank you very much.      Log On


   

Question 454648: I need help with this problem:
Show that the function f(x)=1/(x-2) is one-to-one via cketching its graph. Then find its inverse function.

Thank you very much.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Show that the function f(x)=1/(x-2) is one-to-one via cketching its graph. Then find its inverse function
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As you can see from the graph above, f(x) is a one-to-one function, that is, for each x, there is only one y. To find its inverse, interchange x and y, then solve for y.
y=1/(x-2)
x=1/y-2
xy-2x=1
f(x)(inverse)=(1+2x)/x