(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

find (f-1)'(0) if f'(x) = root(1+x^4)

3. The attempt at a solution

i know (f-1)'(0) = 1 / f'((f-1 (0))

but to find the value of the inverse at 0, i need to find the inverse, for which i need to find the original function by integrating, and i cannot seem to be able to integrate root (1+x^4)

i mean..if I set u to 1+x^4, i get du = 4x^3 dx

but there is nothing other than whats under the root sign in the integral so it doesn't work out , so please guide me :)

and another question

f(x) = (ax + b) / (cx + d)

Determine a, b , c, d for which f = f-1

so i foudn the inverse to be f(x) = (dx - b) / (a - cx)

so i set the two functions equal to each other

(ax + b) / ( cx + d) = (dx - b) / (a - cx)

I have no idea how to figure out the constants now though...After some algebra i get

cx^2 (d+a)+ x(d+a)(d-a) - b(d+a) = 0

so assuming d+ a is not equal to zero, i can simplify to

cx2 +x(d-a)-b = 0

but how the hell do i figre out the constants from this point?

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# Homework Help: Inverse function + integration help

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