Let f : R → R be defined by f(x) = 1 – 5x. Is f a linear transformation?a. f(x + y)f(x) + f(y)+Does f(x + y) = f(x)+ f(y) for all æ, y E R? chooseb. f(cæ) =c(f(x)) =Does f(cæ) = c(f(x)) for all c, x E R? choosec. Is fa linear transformation? choose

Substitute x+y for x in the equation fx=1-5x and simplify to calculate the value of fx+y.…

Answered: Let ƒ : R → R be defined by f(x) = 1 –…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let ƒ : R² → R be defined by ƒ((x, y)) = −6x − 5y + 8. Is ƒ a linear transformation? a. f((x₁, y₁) + (x₂, y2)) = f((x₁, y₁)) + f((x₂, y2)) = + Does f((x₁, y₁) + (x₂, y₂)) = f((x₁, y₁)) + f((x₂, y₂)) for all (x₁, y₁), (x₂, y2) E R²? choose . (Enter x₁ as x1, etc.) b. f(c(x, y)) = c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c E R and all (x, y) = R²? choose c. Isf a linear transformation? choose +
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Let ƒ : R → R be defined by f(x) = 1 – 5x. Is f a linear transformation? a. f(x + y) = f(x) + f(y) + Does f(x + y) = f(x)+ f(y) for all x, y E R? choose %3D b. f(cæ) = c(f(x)) = Does f(cx) = c(f(x)) for all c, x E R? choose %3D c. Is f a linear transformation? choose >