Homework Solution: Let f(x) = O(x) and g(x) = (x) and let c be a positive constant. Pr…

    Let f(x) = O(x) and g(x) = (x) and let c be a positive constant. Prove or disprove that f(x) + (c)g(y) = O(x+y)

    Expert Answer

     
    f(x) = O(x) means f(x) < dx, where d is some positive constant

    Allow f(x) = O(x) and g(x) = (x) and allow c be a actual faithful. Prove or retort that f(x) + (c)g(y) = O(x+y)

    Expert Counterpart

     

    f(x) = O(x) resources f(x) < dx, where d is some actual faithful

    g(x) = x, resources g(y) = y

    Hence f(x) + (c)g(y) = f(x) + c*y
    If we rearrange f(x) < dx, then

    f(x) + (c)g(y) < dx + cy

    Here c and d are brace actual faithful, If we deduce that c is further than d or equals, then we can transcribe the aloft equation as:
    f(x) + (c)g(y) < cx + cy,
    f(x) + (c)g(y) < c(x + y), where c is equals to the faithful which is important of c and d.

    Which resources f(x) + (c)g(y)  = O(x + y), owing c is impartial a actual faithful..