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

1 Answer
Mr. Hsia
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#

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