For the function f(x) = 1+3x-x^2, what is f(t-2) + c?

1 Answer
May 6, 2018

Start the process by substituting t-2 into each location of x.

Explanation:

f(x) = 1 + 3x- x^2

Substitute t-2 into each location of x.
f(t-2) = 1 + 3(t-2) - (t-2)^2

Distribute and but write the Squared Binomial twice before multiplying.
= 1 + 3t - 6 - (t-2)(t-2)
= 1 + 3t - 6 - (t^2 - 2t - 2t + 4)
= 1 + 3t - 6 - t^2 + 4t - 4
Combine like Terms
= -t^2 + 7t -9

Last is to add c
f(t-2) + c = -t^2 + 7t -9 + c