## tangent to inverse function?

Forum for the GRE subject test in mathematics.
hadimotamedi
Posts: 34
Joined: Thu Dec 30, 2010 4:36 am

### tangent to inverse function?

Dear All
For the function 'f' as :
f(x)=x - 1/x ; x >0
for which value of 'a' the line '2y-x=a' is tangent to the curve of f^(-1) (inverse function of f)?
Thank you

hadimotamedi
Posts: 34
Joined: Thu Dec 30, 2010 4:36 am

### Re: tangent to inverse function?

Dear All
I figured out that the question can be solved as the following :
point A(α,β) on the function f(x) curve
point A^'(β,α) on the function f^(-1)(x)
So the slope of tangent to the f^(-1) curve is :
d/dx f^(-1)(β) = 1/d/dxf(α)
And the slope of normal line to the curve is as :
m.m^'= -1
Please comment me if you agree with me.

DDswife
Posts: 160
Joined: Thu Aug 14, 2014 5:29 pm

### Re: tangent to inverse function?

Seems about right to me

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