Answer :
Consider the function f(x) = (x)^2+2 which is equivalent to the given function. In here, we are taking whatever is inside the the parenthesis , we raise it to the power of 2 and then add 2. Note that if we change the x for a t, we will get f(t) = (t)^2+2 which is essencially the same thing.
To solve this question we will use the following formula
[tex](a+b)^2=a^2+2ab+b^2[/tex]So, now we simply replace and simplify:
[tex]f(t+2)=(t+2)^2+2=t^2+2t+2^2+2=t^2+2t+4[/tex][tex]f(t^3+2)=(t^3+2)^2+2=t^6+2t^3+4+2=t^6+2t^3+6[/tex][tex]3f(t)=3(t^2+2)=3t^2+3\cdot2=3t^2+6[/tex][tex](f(t))^2+2=(t^2+2)^2+2=t^4+2t^2+4+2=t^4+2t^2+6[/tex]