Find out these functions' domain and range. To find the domain in each scenario, identify the collection of elements that the function assigned values to. a) the function that assigns to each nonnegative integer its last digit. b) the function that assigns the next largest integer to a positive integer. c) the function that assigns to a bit string the number of one bits in the string. d) the function that assigns to a bit string the number of bits in the string.
a) Domain = N becuase it takes nonnegative integers as input. The Range is the set
c) Here we need to decide what we mean by a bit string. Usually, this means strings of finite
length. For example, we would like to include 0101 as well as 11010010. They have different
lengths, but nontheless we want the function to be able to do something with both of these.
One such way of representing strings of length d is to define the set
The range is all possible output values of this function. In this case, the range is simply N. If we consider the codomain as N, then this function is onto. If on the other hand we had considered the codomain as R or Z, then this function would not be onto.
Here’s a question to think about. Is this function one-to-one? If so, prove it. If not, show
that it isn’t one-to-one. In order to do this, find an
d) The domain is the same as in part (c). The range would be
At the beginning of an environmental study, ad forest covered an area of .Since then, this area has decreased by 4.25% each year.Let t be the number of years since the start of the study.Let y be the area that the forest covers in .
Write an exponential function showing relationship between y and t.
Some friends tell you that they paid $25,000 down on a new house and are to pay $525 per month for 30 years. If interest is 7.8% compounded monthly, what was the selling price of the house? How much interest will they pay in 30 years?
t e^-4t sin3t
Find all whole number solutions of the congruence equation.
3x ≡ 8 mod 11
Use a direct proof to show that the product of two rational numbers is rational.
what is vertex
axis of symmetry
Stairs- Each step of a set of stairs has a tread depth of 11.5 inches and a riser height of 6.5 inches. What is the slope of the set of stairs?
A ball of mass 5 kg is attached to a string of length 10 cm, forming a pendulum. If the string is raised horizontally as shown and released from point A, then what is the v
assume that the random variable Xand Y have the joint pdf f(x,y)=1/2x^3
5=20 mod 4 true or false answer
Pets Plus and Pet Planet are having a sale on the same aquarium. At Pets Plus the aquarium is on sale for 30% off the original price and at Pet Planet it is discounted by 25%.
of Aquarium ($)
If the sales tax rate is 8%, which store has the lower sale price?
, 1 of 1.Select ChoicePets PlusPet Planet has the lower sale price.
Fill in the blank question.
How much will you save by buying the aquarium at the store with the lower sale price? Round to the nearest cent.
Prove that if x is and irrational number and x>0 then route over x is also irrational
A small object has charge Q. Charge q is removed from it and placed on a second small object. The two objects are placed 1 m apart. For the force that each object exerts on the other to be a maximum. q should be: A. 2Q B. Q C. Q/2 D. Q/4 E. 0