Let the function h be defined by `h(x) = sqrt(x) + 2`. If `3h(v) = 18`, then which one of the following is the value of `h(v/4)` ?

Options

A. `-4`
B. `-1`
C. `0`
D. `4`

Answer

To solve the problem step by step, we will follow the given information and the function definition.

### Step 1: Understand the function
The function \( h(x) \) is defined as:
\[ h(x) = \sqrt{x} + 2 \]

### Step 2: Use the given equation
We are given that:
\[ 3h(v) = 18 \]
To find \( h(v) \), we divide both sides by 3:
\[ h(v) = \frac{18}{3} = 6 \]

### Step 3: Set up the equation using the function definition
Since we know \( h(v) = 6 \), we can substitute \( v \) into the function definition:
\[ h(v) = \sqrt{v} + 2 \]
Setting this equal to 6 gives us:
\[ \sqrt{v} + 2 = 6 \]

### Step 4: Solve for \( \sqrt{v} \)
To isolate \( \sqrt{v} \), we subtract 2 from both sides:
\[ \sqrt{v} = 6 - 2 = 4 \]

### Step 5: Square both sides to find \( v \)
Now, we square both sides to solve for \( v \):
\[ v = 4^2 = 16 \]

### Step 6: Find \( h\left(\frac{v}{4}\right) \)
Next, we need to find \( h\left(\frac{v}{4}\right) \). First, calculate \( \frac{v}{4} \):
\[ \frac{v}{4} = \frac{16}{4} = 4 \]

Now we can substitute this value into the function:
\[ h\left(4\right) = \sqrt{4} + 2 \]

### Step 7: Calculate \( h(4) \)
Calculating \( h(4) \):
\[ h(4) = 2 + 2 = 4 \]

### Final Answer
Thus, the value of \( h\left(\frac{v}{4}\right) \) is:
\[ \boxed{4} \]