Gen Math

Question 1

It is a function wherein the set of ordered pairs obtained from by interchanging the first and second elements of each ordered pair.

Answer 1

Inverse Functions

Question 2

Which of the following is the inverse to the function “Multiply x by 2, divide by 3, then subtract 8”?

Answer 2

Add 8 to x, multiply by 3 then divide by 2

Question 3

Which is the inverse relation to the set of ordered pairs

{(–10, 5), (–7, 9), (0, 6), (8, –12)}?

Answer 3

{(5, –10), (9, –7), (6, 0), (–12, 8)}

Question 4

Which is the inverse relation to the set of ordered pairs {(5,2),(7,4),(2,10),(3,8),(0,9)}?

Answer 4

{(2,5),(4,7),(10,2),(8,3),(9,0)}

Question 5

Inverse functions are also known to _______ or to undo the rule.

Answer 5

reverse

Question 6

A pre-paid cellular phone charges 25Php for activation and 0.05Php per minute. The relation of cost to minutes can be defined by the function c(x) = 0.05x + 25. What is the inverse of the function?

Answer 6

f^-1(x) = x/0.05 - 500

Question 7

What is the inverse to the function f(x) = -8 - 5x?

Answer 7

f^-1(x) = -x/5 - 8/5

Question 8

Which of the following is the inverse to the function f(x) = 8x + 6?

Answer 8

f^-1(x) = x-6/8

Question 9

A DVD rental company charges $7 per month plus $2.50 for each rental. The relation can be defined by c(x) = 2.5x +7. Determine the inverse of the function.

Answer 9

c^-1(x) = x/2.5 - 7/2.5

Question 10

The Drama Club is holding a car wash to raise money. The club spent $100 on materials and supplies. The club earns $11.75 for each car they wash. Which of the following is the inverse to the function of how much the club earns per cars washed?

Answer 10

f^-1(x) = x/11.75 + 8.51

Question 11

The Drama Club is holding a car wash to raise money. The club spent $90 on materials and supplies. The club earns $11.25 for each car they wash. Write the function of how much the club earns per cars washed. (Note: Use “x” to represent the number of car wash)

Answer 11

f(x) = 11.25x - 90

Question 12

A DVD rental company charges 150Php per month plus 50Php for each rental. The relation can be defined by c(x) = 50x + 150. Determine the inverse of the function.

Answer 12

c^-1(x) = x/50 - 3

Question 13

The Drama Club is holding a car wash to raise money. The club spent $90 on materials and supplies. The club earns $11.25 for each car they wash. Which of the following is the inverse to the function of how much the club earns per cars washed? (Note: Use “x” to represent the number of car wash)

Answer 13

f^-1(x) = x/11.25 + 8

Question 14

Find the value of x in the equation 3^2/3 = 9x

Answer 14

1/3

Question 15

Find the value of x in the equation 6^–x = 1/216

Answer 15

3

Question 16

Find the value of x in the equation 5^x(x-6) = (1/25)^4

Answer 16

2 and 4

Question 17

Find the value of x in the equation 24x + 1 = 512

Answer 17

2

Question 18

Solve for the inequality 16^2x – 3 ≥ 4^x + 2

Answer 18

[8/3, +∞)

Question 19

Solve for the inequality (1/2)^2x > 2^3

Answer 19

(-∞, -3/2)

Question 20

Solve for the inequality 4^x + 2 < 8^2x

Answer 20

x > 1

Question 21

A population starts with 1 000 individuals and triples every 80 years. Give the exponential model for this situation.

Answer 21

y = 1 000(3)^x/80

Question 22

Suppose that a couple invested Php 50 000 in an account when their child was born, to prepare for the child’s college education. If the average interest rate if 4.4% compounded annually, what exponential model can be used for this situation?

Answer 22

A = 50 000(1.044)^t

Question 23

A population starts with 1 000 individuals and triples every 80 years. What is the size of the population after 100 years?

Answer 23

3948

Question 24

You take out a Php 20 000 loan at 5% interest rate. If the interest is compounded annually, give an exponential model for this situation.

Answer 24

A = 20000(1.05)^t

Question 25

You take out a Php 20 000 loan at 5% interest rate. If the interest is compounded annually, how much will you owe after 10 years?

Answer 25

Php 32 577.89