Lesson 14 : Solving Real-life Problems Involving Inverse Functions

Slide 1

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Real Life Problems of Inverse Functions

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Solving Real-life Problems Involving Inverse Functions

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Cath and Arvin are planning for their wedding. Cath suggested that she wants Casa de Aurora to cater their reception. The reception hall rental fee starts at a flat rate of ₱3,500.00 and an additional rental fee of ₱60.00 per guest. If their budget is limited at ₱20,000.00. Which of the following represents the total rental fee as a function of the number of guests?

a. y = 3500 + 60x

b. y = 3500 – 60x

c. y = 60 + 3500x

d. y = 60 – 3500x

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a. D = {x 𝜖𝜖 N | 0 ≤ x ≤ 275} R = {y 𝜖𝜖 R | 0 ≤ y ≤ 20,000}

b. D = {x 𝜖𝜖 N | 0 ≤ x ≤ 2000} R = {y 𝜖𝜖 R | 0 ≤ y ≤ 10,000}

c. D = {x ϵ N | 0 ≤ x ≤ 160} R = {y ϵ R | 0 ≤ y ≤ 20,000}

d. D = {x ϵ N | 0 ≤ x ≤ 10,000} R = {y 𝜖𝜖 R | 0 ≤ y ≤ 2000}

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Suppose I am travelling at 30 miles per hour, and I want to know how I have gone in x hours. Then, this could be represented by the function 𝑓𝑓(𝑥𝑥)=30𝑥𝑥. Find the inverse of the function.

𝑥/10

𝑥/20

𝑥/30

𝑥/100

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Mark resides in a Quezon City, but he starts a new job in the neighbor city. Every Monday, he drives his new car 80 kilometers from his residence to the office and spends the week in a company apartment. He drives back home every Friday. After 5 weeks of this routinary activity, his car’s odometer shows that he has travelled 1000 kilometers since he bought the car. (Note: He only use his car for his job.) If the mathematical model that gives the distance y covered by the car as a function of x number of weeks is y = 160x + 200. Find its inverse.

(𝑥+150) / 80

(𝑥-180) / 90

(𝑥-510) / 90

(𝑥-200) / 160

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Mark resides in a Quezon City, but he starts a new job in the neighbor city. Every Monday, he drives his new car 80 kilometers from his residence to the office and spends the week in a company apartment. He drives back home every Friday. After 5 weeks of this routinary activity, his car’s odometer shows that he has travelled 1000 kilometers since he bought the car. (Note: He only use his car for his job.) If he travelled 1640 kilometers how many weeks he drives his car?

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A study found that the relationship between the number of hours (x) and the student’s exam scores 𝑓(𝑥) is given by the equation of function 𝑓(𝑥) = 10𝑥 + 55 Using this information, what will be the estimated number of scores of the student if he spent 4 hours in studying?

a. 95

b. 85

c. 75

d. 65

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Which of the following is the inverse 𝑓(𝑥) = 6𝑥 + 5?

(𝑥−5) / 6

(𝑥+5) / 6

(𝑥−2) / 5

(𝑥+2) / 5

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