1. Let f (x) = 3x + 1 and g(x) = -x2 - x. Is it true that f (g(x)) = g(f (x)) for any x ∈ (-∞, ∞)? If not, is there any particular real value of x, which satis?es the above equation?
2. For the following demand and supply functions of a product, state the economically sensible values of price and quantity for which each of them are de?ned. Draw the market diagram for this product with price shown on the vertical axis.
What are the equilibrium price and quantity? Carefully explain why the price you obtained is the equilibrium price.
r qS = -5 + 3p,
qD = 20 - 2p.