Determine if:

f(x) = 1/ x-2 and g(x)= 2x +1/x are inverse functions by computing their composistions.

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- Oct 23rd 2006, 09:56 PMrobinpatrickinverse funtions
Determine if:

f(x) = 1/ x-2 and g(x)= 2x +1/x are inverse functions by computing their composistions. - Oct 24th 2006, 02:22 AMearboth
- Oct 24th 2006, 07:00 AMtopsquark
Please use parenthesis! f(x) = 1/(x-2) not f(x) = (1/x) - 2 and g(x) = (2x + 1)/x, not g(x) = 2x + (1/x).

Multiply top and bottom by x.

= = =

= (Check!)

Again:

Multiply top and bottom by x - 2.

= =

= (Check!)

So f(g(x)) = x and g(f(x)) = x. Thus f and g are inverses.

-Dan