The sum and the difference are (h + k)(2) = 6, (h - k)(3) = 8 and 3h(2) + 2k(3) = 19
The functions are given as:
h(x) = x^2 + 1
k(x) = x - 1
Start by calculating h(2), h(3), k(2) and k(3).
This is done as follows:
h(2) = 2^2 + 1 = 5
h(3) = 3^2 + 1 = 10
k(2) = 2 - 1 = 1
k(3) = 3 - 1 = 2
So, the sum and the differences are:
(h + k)(2) = h(2) + k(2)
This gives
(h + k)(2) = 5 + 1
(h + k)(2) = 6
Also, we have:
(h - k)(3) = h(3) - k(3)
This gives
(h - k)(3) = 10 - 2
(h - k)(3) = 8
Also, we have:
3h(2) + 2k(3) = 3 * h(2) + 2 * k(3)
This gives
3h(2) + 2k(3) = 3 * 5 + 2 * 2
Evaluate
3h(2) + 2k(3) = 19
Hence, the sum and the difference are (h + k)(2) = 6, (h - k)(3) = 8 and 3h(2) + 2k(3) = 19
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