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2 years ago

How do you determine the domain of a function ?

Mathematics

2 answers:

Sunny_sXe [5.5K]2 years ago

8 0

Answer:

Let y = f(x) be a function with an independent variable x and a dependent variable y.

If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that

chosen x-value is said to belong to the domain of f. If there is a requirement that a y-value produced by a function

must be a real number, the following conditions are commonly checked:

1. Denominators cannot equal 0.

2. Radicands (expressions under a radical symbol) of even roots (square roots, etc)

cannot have a negative value.

3. Logarithms can only be taken of positive values.

4. In word problems physical or other real-life restrictions might be imposed, e.g. time is

nonnegative, number of items is a nonnegative integer, etc.

stiks02 [169]2 years ago

5 0

Answer:

the domain is a set of all possible numbers inputs for that function, THe range is all the possible output numbers

i hope this helps

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If a and b are two angles in standard position in Quadrant I, find cos(a+b) for the given function values. sin a=8/17and cos b=1

n200080 [17]

Recall the sum identity for cosine:

cos(a + b) = cos(a) cos(b) - sin(a) sin(b)

so that

cos(a + b) = 12/13 cos(a) - 8/17 sin(b)

Since both a and b terminate in the first quadrant, we know that both cos(a) and sin(b) are positive. Then using the Pythagorean identity,

cos²(a) + sin²(a) = 1 ⇒ cos(a) = √(1 - sin²(a)) = 15/17

cos²(b) + sin²(b) = 1 ⇒ sin(b) = √(1 - cos²(b)) = 5/13

Then

cos(a + b) = 12/13 • 15/17 - 8/17 • 5/13 = 140/221

6 0

2 years ago

The weight of a child in 1990 was 40 lb. By 2005, the child's weight

Maslowich

Answer:

225%

Step-by-step explanation:

1. Divide the new weight by the original weight.

90/40 = 2.25.

2. Multiply by 100 to get the percentage.

2.25 x 100 = 225%

5 0

2 years ago

Select the correct answer.

Colt1911 [192]

Answer: B

Step-by-step explanation:

An individual's effective tax rate is the average tax rate.

7 0

2 years ago

Jonathan records how 90 pupils travelled to school on one day and represents this information on the pie chart below.

xeze [42]

Answer:

86.4

Step-by-step explanation:

First adding up all the percentages on the chart you get 360

Then figuring out what 24° of 360 is

You then get 86.4

4 0

2 years ago

A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess

statuscvo [17]

Let's start by visualising this concept.

Number of grains on square:
1 2 4 8 16 ...

We can see that it starts to form a geometric sequence, with the common ratio being 2.

For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:
$T_n = ar^{n - 1}$
$T_{15} = 2^{14} = 16384$

Thus, there are 16, 384 grains on the fifteenth square.

The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:
$S_n = \frac{a(r^{n} - 1)}{r - 1}$
$S_{15} = \frac{2^{15} - 1}{2 - 1}$
$S_{15} = 2^{15} - 1 = 32767$

Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.

6 0

2 years ago

Read 2 more answers