Question

is the following function a linear transformation?
T:f(negative infinity,infinity) where
T(F(x))=f(x+1)

Answer 1

T(cf(x))=cf(x+1)
=cT(f(x))
where c is a contant.
is it corect?

Answer 2

what are properties of linear transform ??

Answer 3

i dont know myself

Answer 4

T(cU)=cT(U) and T(u + v)=T(u)+T(V)

Answer 5

we cant conclude T(cf(x))=cf(x+1)

Answer 6

why?

Answer 7

our variable is x here not the hole thing...to my understanding the best we can do\[T(f(cx))=f(cx+1)=???\]

Answer 8

sorry i have no idea

@estudier

Answer 9

thanks @mukushla

Answer 10

@TuringTest ,any idea

Answer 11

@satellite73 plz look at this

Answer 12

@jacobian your analysis of the transformation obeying the scalar multiplication rule is correct
the transformation is to add one to the argument

Answer 13

\[T(f(x))=f(x+1)\]\[T(cf(x))=cf(x+1)\]\[cT(f(x))=cf(x+1)~~~~~\large\checkmark\]

Answer 14

@jacobian still here?

Answer 15

yah

Answer 16

awesome
for the next part you need to remember that the sum of any two polynomials is another polynomial, so we can always write\[f(x)+g(x)=h(x)\]so bear that in mind....

Answer 17

so\[T[(f(x)+g(x)]=T(h(x))=h(x+1)\]\[=f(x+1)+g(x+1)=T(f(x))+T(g(x))~~~~\large\checkmark\]catch that?

Answer 18

yes ,thanks a bulk

Answer 19

anytime :)