Determine which of the following functions are one-to-one. DA. f: R R defined by f() = x2. B. f: R → R defined by f(x, y, z) = (x + y, Y + z, x + z). Mc. f: R³ → R³ defined by f(, y, z) = (x – y, y – z, x – z). D. f: R2 R² defined by f(x, y) = (x + y, 2x + 2y). E. f: R→ R² defined by f(x, y) = (x + y, x – y).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Determine which of the following functions are one-to-one.
A. f: R R defined by f(x) = x².
B. f: R R defined by f(x, y, z) = (x + y,Y + z, x + z).
c. f: R→ R³ defined by f(x, y, z) = (x – y, Y – 2, x – z).
D. f: R2R defined by f(x, y) = (x+ y, 2x + 2y).
E. f : R2 R2 defined by f(x, y) = (x + y, x – y).
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->
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Transcribed Image Text:Determine which of the following functions are one-to-one. A. f: R R defined by f(x) = x². B. f: R R defined by f(x, y, z) = (x + y,Y + z, x + z). c. f: R→ R³ defined by f(x, y, z) = (x – y, Y – 2, x – z). D. f: R2R defined by f(x, y) = (x+ y, 2x + 2y). E. f : R2 R2 defined by f(x, y) = (x + y, x – y). %3D -> %3D
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