The operation (h-g)(n) is based on the subtraction of the function g(n) from h(n). To solve, we need to make the calculations step by step.
The definitions for h(n) and g(n) are as follows:
h(n) = n^(3)-2
g(n) = -4n-5
To find the result of the operation h(n) - g(n), which is denoted as (h-g)(n), we subtract g(n) from h(n):
(h-g)(n) = h(n) - g(n) = ( n^(3) - 2 ) - ( -4n - 5 )
Choosing to perform operations in brackets first (following the BEDMAS/BODMAS order of operations), we rearrange the equation:
(h-g)(n) = n^(3) - 2 + 4n + 5
Adding like terms together results in:
(h-g)(n) = n^(3) + 4n + 3
So, (h-g)(n) = n^(3) + 4n + 3. This is the outcome of the operation of the subtraction of g(n) from h(n).