Let ƒ : R → R³ be defined by f(x) = (x, −9x², 3x). Is ƒ a linear transformation? a. f(x + y) = f(x) + f(y) + Does f(x + y) = f(x) + f(y) for all x, y = R? choose = b. f(cx) = c(f(x)) Does f(cx) = c(f(x)) for all c, x = R? choose = c. Is f a linear transformation? choose

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 41E
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Let ƒ : R → R³ be defined by f(x) = (x, −9x², 3x). Is ƒ a linear transformation?
a. f(x + y) =
f(x) + f(y)
+
Does f(x + y) = f(x) + f(y) for all x, y = R? choose
b. f(cx) =
c(f(x)) =
=
Does f(cx)
=
=
c(f(x)) for all c, x = R? choose
c. Is f a linear transformation? choose
Transcribed Image Text:Let ƒ : R → R³ be defined by f(x) = (x, −9x², 3x). Is ƒ a linear transformation? a. f(x + y) = f(x) + f(y) + Does f(x + y) = f(x) + f(y) for all x, y = R? choose b. f(cx) = c(f(x)) = = Does f(cx) = = c(f(x)) for all c, x = R? choose c. Is f a linear transformation? choose
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