Question
Let \( h(x)=x+9 \) and \( g(x)=\sqrt{x-6} \). Find \( (h-g)(-1) \). Select the correct choice below and fill in any answer boxes within your choice. A. \( (h-g)(-1)=\square \) (Simplify your answer. Type an integer or a fraction.) B. The function value does not exist.
Ask by Bright Hanson. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The function value does not exist.
Solution
We are given h(x) = x + 9 and g(x) = √(x – 6). To find (h – g)(-1), we compute:
h(-1) = -1 + 9 = 8.
g(-1) = √(-1 – 6) = √(-7).
Since √(-7) is not a real number, g(-1) is undefined in the real number system. Therefore, (h – g)(-1) is undefined.
The correct choice is B. The function value does not exist.
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Simplify this solution Beyond the Answer
To find \( (h-g)(-1) \), we first need to compute \( h(-1) \) and \( g(-1) \). \( h(x) = x + 9 \) So, \( h(-1) = -1 + 9 = 8 \). Now for \( g(x) = \sqrt{x - 6} \): Since \( -1 - 6 = -7 \), this means \( g(-1) = \sqrt{-7} \), which is not a real number. Now, we can compute \( (h-g)(-1) \): \[ (h-g)(-1) = h(-1) - g(-1) = 8 - \text{(not defined)} \] Thus, the correct choice is: B. The function value does not exist.
