solve simple problem.

[devnarayan]

δ(-t-t0)*x(t0-t) (where * for convolution) ,what is it solution please select the option (a)x(2t0-t) (b)x(t-2t0) (c) x(-t) (d)x(t)
i had got option 'a' but answer provided is 'c'. how it can be

 

[bene_]

the function x(-t) is just shifted by t0 in one direction and by the convolution with the dirac, which is shifted into the other direction also by t0, it will be in x(-t) will be at its original position again.

 

[devnarayan]

sir but when i solve mathematically we get another solution please see picture attachement and comment on that. thank you very much sir.

 

[rajanarender_suram]

δ(-t-t0)*x(t0-t);
remenber δ(t-t0)*x(t)=x(t-t0);
let -t =T
than
δ(-t-t0)*x(t0-t) = δ(T-t0)*x(t0+T)=x(t0+T-t0)=x(T)=x(-t)