Final answer:
To find g(x) for different values of x using the given function g(x) = {- 1/2 x + 9 if x ≤ 7, √x-7 if x ≥ 7.
Step-by-step explanation:
To find g(-7), we substitute -7 into the function g(x). Since -7 is less than or equal to 7, we use the first part of the function, g(x) = -1/2x + 9. Thus, g(-7) = -1/2(-7) + 9 = 13.5.
To find g(0), we substitute 0 into the function g(x). Since 0 is less than or equal to 7, we use the first part of the function, g(x) = -1/2x + 9. Thus, g(0) = -1/2(0) + 9 = 9.
To find g(7), we substitute 7 into the function g(x). Since 7 is equal to 7, we use the second part of the function, g(x) = √x-7. Thus, g(7) = √7-7 = 0.
To find g(14), we substitute 14 into the function g(x). Since 14 is greater than 7, we use the second part of the function, g(x) = √x-7. Thus, g(14) = √14-7 = √7.
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