Choose The Composition Function That Gives The Final Sale Price After A $10%$ Discount Is Followed By A $$ 150 150 150 $ Coupon.A. C ( P ( X ) ) = 0.9 X − 150 C(P(x)) = 0.9x - 150 C ( P ( X )) = 0.9 X − 150 B. P ( C ( X ) ) = 0.9 X − 150 P(C(x)) = 0.9x - 150 P ( C ( X )) = 0.9 X − 150 C. $C(P(x)) = 1.9x -

When it comes to calculating the final sale price after applying a discount and a coupon, it's essential to understand the composition of functions involved. In this article, we will explore the correct composition function that gives the final sale price after a $10$ discount is followed by a $$150$ coupon.

Understanding the Composition of Functions

The composition of functions is a fundamental concept in mathematics that involves combining two or more functions to create a new function. In this case, we have two functions: the discount function and the coupon function. The discount function reduces the price by $10\%$, while the coupon function subtracts a fixed amount of $$150$ from the price.

Discount Function

The discount function can be represented as $D(x) = 0.9x$, where $x$ is the original price. This function reduces the price by $10\%$ by multiplying the original price by $0.9$.

Coupon Function

The coupon function can be represented as $C(x) = x - 150$, where $x$ is the price after the discount. This function subtracts a fixed amount of $$150$ from the price.

Composition of Functions

Now, let's consider the composition of functions. We want to find the final sale price after applying the discount and the coupon. To do this, we need to compose the two functions.

There are two possible compositions:

A. $C(P(x)) = 0.9x - 150$ B. $P(C(x)) = 0.9x - 150$ C. $C(P(x)) = 1.9x - 150$

Analyzing the Compositions

Let's analyze each composition:

A. $C(P(x)) = 0.9x - 150$

In this composition, we first apply the discount function $P(x) = 0.9x$ to get the price after the discount. Then, we apply the coupon function $C(x) = x - 150$ to get the final sale price.

B. $P(C(x)) = 0.9x - 150$

In this composition, we first apply the coupon function $C(x) = x - 150$ to get the price after the coupon. Then, we apply the discount function $P(x) = 0.9x$ to get the final sale price.

C. $C(P(x)) = 1.9x - 150$

In this composition, we first apply the discount function $P(x) = 0.9x$ to get the price after the discount. Then, we apply the coupon function $C(x) = x - 150$ to get the final sale price.

Choosing the Correct Composition

Now, let's choose the correct composition function.

The correct composition function is the one that first applies the discount function and then applies the coupon function. This is because the discount function reduces the price by $10\%$, and the coupon function subtracts a fixed amount of $$150$ from the price.

Therefore, the correct composition function is:

C(P(x)) = 0.9x - 150

This composition function first applies the discount function $P(x) = 0.9x$ to get the price after the discount. Then, it applies the coupon function $C(x) = x - 150$ to get the final sale price.

Conclusion

In conclusion, the correct composition function that gives the final sale price after a $10\%$ discount is followed by a $$150$ coupon is:

C(P(x)) = 0.9x - 150

This composition function first applies the discount function $P(x) = 0.9x$ to get the price after the discount. Then, it applies the coupon function $C(x) = x - 150$ to get the final sale price.

Final Answer

In this article, we will address some of the most frequently asked questions related to the composition function that gives the final sale price after a $10\%$ discount is followed by a $$150$ coupon.

Q: What is the correct composition function?

A: The correct composition function is C(P(x)) = 0.9x - 150. This function first applies the discount function $P(x) = 0.9x$ to get the price after the discount. Then, it applies the coupon function $C(x) = x - 150$ to get the final sale price.

Q: Why is the correct composition function C(P(x)) = 0.9x - 150?

A: The correct composition function is C(P(x)) = 0.9x - 150 because it first applies the discount function $P(x) = 0.9x$ to get the price after the discount. Then, it applies the coupon function $C(x) = x - 150$ to get the final sale price. This is the correct order of operations because the discount function reduces the price by $10\%$, and the coupon function subtracts a fixed amount of $$150$ from the price.

Q: What is the difference between C(P(x)) = 0.9x - 150 and P(C(x)) = 0.9x - 150?

A: The difference between C(P(x)) = 0.9x - 150 and P(C(x)) = 0.9x - 150 is the order of operations. C(P(x)) = 0.9x - 150 first applies the discount function $P(x) = 0.9x$ to get the price after the discount. Then, it applies the coupon function $C(x) = x - 150$ to get the final sale price. On the other hand, P(C(x)) = 0.9x - 150 first applies the coupon function $C(x) = x - 150$ to get the price after the coupon. Then, it applies the discount function $P(x) = 0.9x$ to get the final sale price.

Q: Why is C(P(x)) = 1.9x - 150 incorrect?

A: C(P(x)) = 1.9x - 150 is incorrect because it first applies the discount function $P(x) = 0.9x$ to get the price after the discount. However, the discount function reduces the price by $10\%$, which means the price after the discount is $0.9x$, not $1.9x$. Therefore, the correct composition function is C(P(x)) = 0.9x - 150.

Q: How do I apply the composition function C(P(x)) = 0.9x - 150 in real-life scenarios?

A: To apply the composition function C(P(x)) = 0.9x - 150 in real-life scenarios, you can follow these steps:

1. Determine the original price $x$.
2. Apply the discount function $P(x) = 0.9x$ to get the price after the discount.
3. Apply the coupon function $C(x) = x - 150$ to get the final sale price.

For example, if the original price is $$100$, the price after the discount is $$90$ ($0.9 \times 100$). Then, the final sale price is $$60$ ($90 - 150$).

Conclusion

In conclusion, the correct composition function that gives the final sale price after a $10\%$ discount is followed by a $$150$ coupon is C(P(x)) = 0.9x - 150. This function first applies the discount function $P(x) = 0.9x$ to get the price after the discount. Then, it applies the coupon function $C(x) = x - 150$ to get the final sale price.