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.