+24 1. The function f(xy) accepts an ordered pair as input and gives another ordered pair as output. It is defined according to the following rules: x>4, f(x,y) = (x - 4,y). If , . If x<=4 but y>4, f(x,y) = (x,y - 4). Otherwise, f(x,y) = (x + 5, y + 6). A robot starts by moving to the point (1,1). Every time it arrives at a point (x,y), it applies f to that point and then moves to f(x,y). If the robot runs forever, how many different points will it visit?
2. Let f(x) = 2x + 7 and g(x) = 3x + c. Find c if \((f \circ g)(x) = (g \circ f)(x)\) for all x.
3. Let \(x\mathbin{\spadesuit}y = x^2/y\) for all x and y such that \(y\neq 0\). Find all values of a such that \(a\mathbin{\spadesuit} 3 = 9 \).
4. If \(f(a) = \frac{1}{1-a}\), find the product \(f^{-1}(a) \times a \times f(a)\).
+33616 Question1.
(1,1) → (6,7) → (2,7) → (2,3) → (7,9) → (3,9) → (3,5) → (3,1) → (8,7) → (4,7) → (4,3) → (9,9) → (5,9) → (1,9) → (1,5) → (1,1)
15 different points.
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