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If I have a vector say for example $\vec{r}(t)=<t,t^2,3t^2>$ and a function $f(x,y,z)=\sqrt{1+30x^2+10y}$ whats the best way to express $f(x,y,z)$ as a function of the parameter $t$?

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It is your duty to upvote answers to your questions (if they are helpful) and accept the best answer if there is anyone deserving it. Otherwise provide more detailed explanation what you expect. –  Artes Dec 7 '13 at 2:02

1 Answer 1

You can use @@:

r[t_] := {t, t^2, 3 t^2}
f[x_, y_, z_] := Sqrt[1 + 30 x^2 + 10 y]
f @@ r[t]
(* Sqrt[1 + 40 t^2] *)

But what is best depends on what you want to do with it later

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