Let R denote the set of real numbers. Let f: R x R -> R x R be a bijective…
1996
Let R denote the set of real numbers. Let f: R x R -> R x R be a bijective function defined by f(x, y) = (x + y, x - y). The inverse function of f is given by:
- A.
f inverse(x, y) = (1/(x + y), 1/(x - y))
- B.
f inverse(x, y) = (x - y, x + y)
- C.
f inverse(x, y) = ((x + y)/2, (x - y)/2)
- D.
f inverse(x, y) = (2(x - y), 2(x + y))
Attempted by 33 students.
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Correct answer: C
let the output point be (x, y), and suppose it came from an input point (a, b).
then x = a + b and y = a - b.
adding the two equations gives x + y = 2a, so a = (x + y)/2.
subtracting the second equation from the first gives x - y = 2b, so b = (x - y)/2.
therefore, f inverse(x, y) = ((x + y)/2, (x - y)/2), which matches option c.