If #h(n) = n^2-4n# and #g(n) = -2n-5#, what is #(h+g)(n/2)#?

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Answer 1 · 2017-03-06T13:03:33

#(h + g)(n/2) = n^2/4 - 3n - 5#

#(h + g)(n/2) = h(n/2) + g(n/2)#

If #h(n) = n^2 - 4n# then

#h(n/2) = (n/2)^2 - 4(n/2)#

#h(n/2) = n^2/4 - 2n#

If #g(n) = -2n - 5# then

#g(n/2) = -2(n/2) - 5#

#g(n/2) = -n - 5#

Therefore:

#(h + g)(n/2) = h(n/2) + g(n/2) = (n^2/4 - 2n) + (-n - 5)#

#(h + g)(n/2) = n^2/4 - 2n - n - 5#

#(h + g)(n/2) = n^2/4 - 3n - 5#