To solve this, we begin by substitifying x = 1/2 into our function f(x).
So, f(x) when x = 1/2 is f(1/2) = - (1/2)^3 + (7/8)*(1/2).
We need to calculate each term separately.
First term is - (1/2)^3. When we cube the 1/2, we get 1/8 and the negative sign in front gives -1/8.
Next, for the second term, we have (7/8) times (1/2). This multiplication gives us 7/16.
Now, we add these two results together: from -1/8 add 7/16.
Multiplying the numbers to have the same denominator, quick adjustment brings -1/8 to -2/16. So the final expression is -2/16 + 7/16.
Adding these together, we have 5/16. Therefore, f(1/2) equals to 5/16.
However, as decimal, 5/16 is equivalent to 0.3125. Therefore, f(1/2) or the value of the function when x = 1/2 is 0.3125.
That's our final answer.