Answer
a) f(x)=10
The f(x) =10 function is constant. In Big O notation, f(x)=10 doesn't depend on x; it remains constant regardless of the value of x .
O(1) represents that the function doesn't grow with the input size.
Hence,
f(x)=10 is O(1) or it can be written as O(x0).
Work Step by Step
b) f(x)=3x+7
To determine if f(x)=3x+7 is O(x), we need to see if it satisfies the condition ∣f(x)∣≤C⋅∣x∣.
f(x)=3x+7
For this function to be O(x), it should be bounded by a constant multiple of x.
In f(x)=3x is indeed O(x) because it is directly proportional to x with a constant factor of 3.
Hence it satisfies the condition for being O(x).
