it is the question related to derivaqtives and it is little bit complicated

Question

Find f^-1and find the derivative of f^-1implicitly.

a)5x³+x-7

b)1/x² ,x>0

Answer 1

f(x) = 1/x^2

y=1/x^2 to find the inverse switch x and y and then solve for y

x=1/y^2

y^2 = 1/x

y = sqr(1/x) = 1/sqrx = x^(-1/2)

f^-1(x) = 1/sqrx = (sqrx)/x You could say + or -, but then it's not a function. It's an inverse, but not an inverse function. The notation "f" suggests we're dealing with functions.

y' = -(1/2)x^(-3/2) =-1/2xsqrx