Difficult question? (1 Viewer)

[Makematics]

This is from last year's UNSW maths comp paper, and i'm really keen to get solution for it.
Find an example of an inverse function f(x) such that its derivative is the same as its inverse.

 

[omgiloverice]

I tried...

 

[seanieg89]

Look for a solution of the form where a and p are two real constants to be determined. It is easy from here.

 

[Makematics]

Look for a solution of the form where a and p are two real constants to be determined. It is easy from here.

:'( im still having difficulty... tried stuff like x^e etc. but doesnt seem to work.

 

[SpiralFlex]

pax^(p-1) is equal to something and that something is-----------

 

[Makematics]

(x/a)^(1/p)? ive tried messing around with this and have gotten nowhere

 

[humphdogg]

Stop trying to guess examples. Use the fact that pax^{p-1} must be equal to a^{1/p} x^{1/p}. Solve for the possible values of p by comparing exponents of x. Then solve for a by comparing coefficients. This will give you an answer.