If $f(x) = \sqrt{x} + 12$ And $g(x) = 2 \sqrt{x}$, What Is The Value Of $(f-g)(144$\]?A. -84 B. -60 C. 0 D. 48

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Understanding the Functions

To find the value of $(f-g)(144)$, we first need to understand the given functions $f(x)$ and $g(x)$. The function $f(x)$ is defined as $f(x) = \sqrt{x} + 12$, where $\sqrt{x}$ represents the square root of $x$. On the other hand, the function $g(x)$ is defined as $g(x) = 2 \sqrt{x}$, which is twice the square root of $x$.

Calculating the Difference

The expression $(f-g)(144)$ represents the difference between the functions $f(x)$ and $g(x)$ evaluated at $x=144$. To find this difference, we need to substitute $x=144$ into the functions $f(x)$ and $g(x)$ and then subtract the result of $g(x)$ from the result of $f(x)$.

Evaluating $f(144)$

To evaluate $f(144)$, we substitute $x=144$ into the function $f(x) = \sqrt{x} + 12$. This gives us $f(144) = \sqrt{144} + 12$. Since $\sqrt{144} = 12$, we have $f(144) = 12 + 12 = 24$.

Evaluating $g(144)$

To evaluate $g(144)$, we substitute $x=144$ into the function $g(x) = 2 \sqrt{x}$. This gives us $g(144) = 2 \sqrt{144}$. Since $\sqrt{144} = 12$, we have $g(144) = 2 \times 12 = 24$.

Finding the Difference

Now that we have evaluated $f(144)$ and $g(144)$, we can find the difference $(f-g)(144)$ by subtracting $g(144)$ from $f(144)$. This gives us $(f-g)(144) = f(144) - g(144) = 24 - 24 = 0$.

Conclusion

In conclusion, the value of $(f-g)(144)$ is $0$. This is because the functions $f(x)$ and $g(x)$ evaluated at $x=144$ are equal, resulting in a difference of $0$.

Step-by-Step Solution

Here is the step-by-step solution to the problem:

1. Evaluate $f(144)$ by substituting $x=144$ into the function $f(x) = \sqrt{x} + 12$.
2. Evaluate $g(144)$ by substituting $x=144$ into the function $g(x) = 2 \sqrt{x}$.
3. Find the difference $(f-g)(144)$ by subtracting $g(144)$ from $f(144)$.

Final Answer

The final answer is $\boxed{0}$.

Discussion

The problem requires us to find the value of $(f-g)(144)$, which involves evaluating the functions $f(x)$ and $g(x)$ at $x=144$ and then finding the difference between the two results. The key to solving this problem is to understand the definitions of the functions $f(x)$ and $g(x)$ and to carefully evaluate the expressions $f(144)$ and $g(144)$. By following the step-by-step solution outlined above, we can arrive at the correct answer of $0$.

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Understanding the Functions

To find the value of $(f-g)(144)$, we first need to understand the given functions $f(x)$ and $g(x)$. The function $f(x)$ is defined as $f(x) = \sqrt{x} + 12$, where $\sqrt{x}$ represents the square root of $x$. On the other hand, the function $g(x)$ is defined as $g(x) = 2 \sqrt{x}$, which is twice the square root of $x$.

Calculating the Difference

The expression $(f-g)(144)$ represents the difference between the functions $f(x)$ and $g(x)$ evaluated at $x=144$. To find this difference, we need to substitute $x=144$ into the functions $f(x)$ and $g(x)$ and then subtract the result of $g(x)$ from the result of $f(x)$.

Evaluating $f(144)$

To evaluate $f(144)$, we substitute $x=144$ into the function $f(x) = \sqrt{x} + 12$. This gives us $f(144) = \sqrt{144} + 12$. Since $\sqrt{144} = 12$, we have $f(144) = 12 + 12 = 24$.

Evaluating $g(144)$

To evaluate $g(144)$, we substitute $x=144$ into the function $g(x) = 2 \sqrt{x}$. This gives us $g(144) = 2 \sqrt{144}$. Since $\sqrt{144} = 12$, we have $g(144) = 2 \times 12 = 24$.

Finding the Difference

Now that we have evaluated $f(144)$ and $g(144)$, we can find the difference $(f-g)(144)$ by subtracting $g(144)$ from $f(144)$. This gives us $(f-g)(144) = f(144) - g(144) = 24 - 24 = 0$.

Conclusion

In conclusion, the value of $(f-g)(144)$ is $0$. This is because the functions $f(x)$ and $g(x)$ evaluated at $x=144$ are equal, resulting in a difference of $0$.

Step-by-Step Solution

Here is the step-by-step solution to the problem:

1. Evaluate $f(144)$ by substituting $x=144$ into the function $f(x) = \sqrt{x} + 12$.
2. Evaluate $g(144)$ by substituting $x=144$ into the function $g(x) = 2 \sqrt{x}$.
3. Find the difference $(f-g)(144)$ by subtracting $g(144)$ from $f(144)$.

Final Answer

The final answer is $\boxed{0}$.

Discussion

The problem requires us to find the value of $(f-g)(144)$, which involves evaluating the functions $f(x)$ and $g(x)$ at $x=144$ and then finding the difference between the two results. The key to solving this problem is to understand the definitions of the functions $f(x)$ and $g(x)$ and to carefully evaluate the expressions $f(144)$ and $g(144)$. By following the step-by-step solution outlined above, we can arrive at the correct answer of $0$.

Q&A

Q: What is the value of $(f-g)(144)$?

A: The value of $(f-g)(144)$ is $0$.

Q: How do we evaluate $f(144)$?

A: To evaluate $f(144)$, we substitute $x=144$ into the function $f(x) = \sqrt{x} + 12$. This gives us $f(144) = \sqrt{144} + 12$. Since $\sqrt{144} = 12$, we have $f(144) = 12 + 12 = 24$.

Q: How do we evaluate $g(144)$?

A: To evaluate $g(144)$, we substitute $x=144$ into the function $g(x) = 2 \sqrt{x}$. This gives us $g(144) = 2 \sqrt{144}$. Since $\sqrt{144} = 12$, we have $g(144) = 2 \times 12 = 24$.

Q: What is the difference between $f(144)$ and $g(144)$?

A: The difference between $f(144)$ and $g(144)$ is $0$, since $f(144) = 24$ and $g(144) = 24$.

Q: What is the final answer to the problem?

A: The final answer to the problem is $\boxed{0}$.

Q: What is the key to solving this problem?

A: The key to solving this problem is to understand the definitions of the functions $f(x)$ and $g(x)$ and to carefully evaluate the expressions $f(144)$ and $g(144)$.

Q: What is the step-by-step solution to the problem?

A: The step-by-step solution to the problem is:

1. Evaluate $f(144)$ by substituting $x=144$ into the function $f(x) = \sqrt{x} + 12$.
2. Evaluate $g(144)$ by substituting $x=144$ into the function $g(x) = 2 \sqrt{x}$.
3. Find the difference $(f-g)(144)$ by subtracting $g(144)$ from $f(144)$.

Additional Resources

• Mathematics
• Functions
• Square Root

Conclusion

In conclusion, the value of $(f-g)(144)$ is $0$. This is because the functions $f(x)$ and $g(x)$ evaluated at $x=144$ are equal, resulting in a difference of $0$. The key to solving this problem is to understand the definitions of the functions $f(x)$ and $g(x)$ and to carefully evaluate the expressions $f(144)$ and $g(144)$. By following the step-by-step solution outlined above, we can arrive at the correct answer of $0$.