Question

5. The function f(x) is defined by f(x)= [(x²-6,x<0) and (10-x,x>or equal to 0) state the domain and the range

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Answer 1

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}