Let f: (1, infinity) -> reals be defined by f(x) = ln(x). Determine whether f is injective/surjective/bijective.
Find a bijection from the integers to the even integers.
If f: Z -> 2Z is defined by f(x) = 2x, find the inverse of f.
Let g: R -> R be defined by g(x) = 2x+5 . Prove g bijective and find the inverse of g.
Let f: R -> R with f(x) = x^2, g: R -> R with g(x) = 2x+1, h: [0, infinity) -> reals with h(x) = sqrt(x). Find the compositions of:
f and g,
g and f,
f and h,
h and f.