Given that f(x)= -x^2+6x-11

Find f(t-3)

x is just a place holder -- you can replace it with whatever you wish. So,

f(t-3) = -(t-3)^2 + 6(t-3) - 11
now just expand that out

To find f(t-3), we need to substitute (t-3) in place of x in the function f(x)= -x^2+6x-11.

Substituting (t-3) in place of x, we get:

f(t-3) = -(t-3)^2 + 6(t-3) - 11

Now, we can simplify the expression by expanding and simplifying:

f(t-3) = -(t^2 - 6t + 9) + 6t - 18 - 11

Next, distribute the negative sign across the squared term:

f(t-3) = -t^2 + 6t - 9 + 6t - 18 - 11

Combine like terms:

f(t-3) = -t^2 + 12t - 38

Therefore, f(t-3) = -t^2 + 12t - 38.