U Calculus Question 03

6. Determine whether or not the given function is one-to-one and, if so, find the inverse. If f has an inverse, give the domain of f^-1
f(x) = (4x – 1)^3
f(x) = 1 / (1 – x) – 1
Show that the composition of two one-to-one functions, f and g, is one to one, and expression (f . g)^-1 in terms of f-1 and g-1

Given function f is differentiable. Verify that f has an inverse and find (f^-1)’(c)
f(x) = sinx, - pi/2 < x < pi/2; c = -1/2
f(x) = x^5 + 2x^3 + 2x; c = -5