Final answer:
To find the values of a and b for the given function, we need to consider two different cases for x: x > 0 and x ≤ 0. For x > 0, the function is f(x) = sin(ax²) / (3x), and for x ≤ 0, the function is f(x) = (1-x)² + b. In both cases, a and b can be any real numbers.
Step-by-step explanation:
To find the values of a and b for the given function, we need to consider the two different cases for x: x > 0 and x ≤ 0. For x > 0, the function is f(x) = sin(ax²) / (3x). For x ≤ 0, the function is f(x) = (1-x)² + b. Let's solve for each case separately.
Case 1: x > 0
Since x > 0, we can simplify the function to f(x) = sin(ax²) / (3x).
This function does not have any specific values for a and b as they can be any real numbers.
Case 2: x ≤ 0
Since x ≤ 0, we can simplify the function to f(x) = (1-x)² + b.
Again, this function does not have any specific values for a and b as they can be any real numbers.