Thread: Integration question

Question: The function f with the domain: x is greater than 1/2 is defined by f(x)=4x(2x-1)^7. Given that f(1)=4, find the value of d/dx{f^-1(x)} when x=4.

I would try and find the inverse function of f(x), but im not sure how exactly this is related to integration in my textbook chapter. Can anyone shed some light as to which direction i proceed in finding d/dx{f^-1(x)}? Unsure how to start this one. Thanks

Hello !

Originally Posted by fire.garden

Question: The function f with the domain: x is greater than 1/2 is defined by f(x)=4x(2x-1)^7. Given that f(1)=4, find the value of d/dx{f^-1(x)} when x=4.

I would try and find the inverse function of f(x), but im not sure how exactly this is related to integration in my textbook chapter. Can anyone shed some light as to which direction i proceed in finding d/dx{f^-1(x)}? Unsure how to start this one. Thanks

Let's do it in a general case first.

Say you have a function f. Its inverse function is such that
Differentiate implicitly (use chain rule for the left-hand side of the equation) :



Hence

Let :

Now, how do you calculate ?
By solving or by using the information you're given :
Hence and :



Can you take it from here ?

Thanks! i think i can do it now