The domain of f(x) is the set of all values that x can take. Since the function has two pieces or segments, we need to consider the domain for each one separately.
For the first segment, we have x ≤ 6. This means that any value of x less than or equal to 6 is in the domain of this segment. For the second segment, we have x ≥ 0. This means that any value of x greater than or equal to 0 is in the domain of this segment. Therefore, the domain of f(x) is:
Domain = {x : x ≤ 6, x ≥ 0}
The range of f(x) is the set of all possible output values of the function. We can see that f(x) takes on values in two different intervals. For x ≤ 6, the function takes on values between 6 - x and 0. For x ≥ 0, the function takes on values between 10 - x and 0. Therefore, the range of f(x) is:
Range = {f(x) : 0 ≤ f(x) ≤ 6, or 0 ≤ f(x) ≤ 10}