Question
\( 1 \leftarrow \) Given that \( h(x)=x+2 \) and \( g(x)=\sqrt{x-4} \), find \( \left(\frac{g}{h}\right)(4) \), if it exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \left(\frac{g}{h}\right)(4)=\square \). (Simplify your answer.) B. The function value does not exist.
Ask by Schofield Robbins. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \left(\frac{g}{h}\right)(4) = 0 \)
Solution
To evaluate (g/h)(4), we first compute g(4) and h(4).
Given g(x) = √(x – 4), we have:
g(4) = √(4 – 4) = √0 = 0.
Given h(x) = x + 2, we have:
h(4) = 4 + 2 = 6.
Now, (g/h)(4) = g(4) / h(4) = 0 / 6 = 0.
Thus, the correct choice is:
A. (g/h)(4) = 0.
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Simplify this solution The Deep Dive
To find \( \left(\frac{g}{h}\right)(4) \), we first need to compute \( g(4) \) and \( h(4) \). Calculating \( h(4) \): \[ h(4) = 4 + 2 = 6 \] Now calculating \( g(4) \): \[ g(4) = \sqrt{4 - 4} = \sqrt{0} = 0 \] Now we can find \( \left(\frac{g}{h}\right)(4) \): \[ \left(\frac{g}{h}\right)(4) = \frac{g(4)}{h(4)} = \frac{0}{6} = 0 \] So, the answer is A. \( \left(\frac{g}{h}\right)(4) = 0 \).
