Which of the functions graphed in Exercises 1–6 are one-to-one, and which are not?

Each of Exercises 25–36 gives a formula for a function y=f(x). In each case, find f^(-1)(x) and identify the domain and range of f^(-1). As a check, show that f(f^(-1)(x))=f^(-1)(f(x))=x.

f(x) = x² − 2x, x ≤ 1

Each of Exercises 19–24 gives a formula for a function y=f(x) and shows the graphs of f and f^(-1). Find a formula for f^(-1) in each case.

f(x)=x²+1, x≥0

"In Exercises 59–86, find the derivative of y with respect to the given independent variable.

63. y = x^π"

Evaluate the integrals in Exercises 39–56.

39. ∫(from -3 to -2)dx/x

Solve the differential equation in Exercises 9–22.

19. y²(dy/dx) = 3x²y³ - 6x²

84. Find lim(x→∞) (√(x² + 1) - √x).