Please help me do this problem.

Find the domain of the function y = 3 tan(23x)

solmaris [256]

Answer:

$\mathbb{R} \backslash \displaystyle \left\lbrace \left. \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right) \; \right| k \in \mathbb{Z} \right\rbrace$ .

In other words, the $x$ in $f(x) = 3\, \tan(23\, x)$ could be any real number as long as $x \ne \displaystyle \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right)$ for all integer $k$ (including negative integers.)

Step-by-step explanation:

The tangent function $y = \tan(x)$ has a real value for real inputs $x$ as long as the input $x \ne \displaystyle k\, \pi + \frac{\pi}{2}$ for all integer $k$ .

Hence, the domain of the original tangent function is $\mathbb{R} \backslash \displaystyle \left\lbrace \left. \left(k\, \pi + \frac{\pi}{2}\right) \; \right| k \in \mathbb{Z} \right\rbrace$ .

On the other hand, in the function $f(x) = 3\, \tan(23\, x)$ , the input to the tangent function is replaced with $(23\, x)$ .

The transformed tangent function $\tan(23\, x)$ would have a real value as long as its input $(23\, x)$ ensures that $23\, x\ne \displaystyle k\, \pi + \frac{\pi}{2}$ for all integer $k$ .

In other words, $\tan(23\, x)$ would have a real value as long as $x\ne \displaystyle \frac{1}{23} \, \left(k\, \pi + \frac{\pi}{2}\right)$ .

Accordingly, the domain of $f(x) = 3\, \tan(23\, x)$ would be $\mathbb{R} \backslash \displaystyle \left\lbrace \left. \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right) \; \right| k \in \mathbb{Z} \right\rbrace$ .

4 0

2 years ago

Supposed a Visa card had a credit card number of 4162 0012 3456789a where a is the check number what is the check number? A) 0 B

MrMuchimi

Answer:

Option B) 3

Step-by-step explanation:

we have the number

4162 0012 3456 789a

Find the value of a (check number)

step 1

Multiply every even-position digit (when counted from the right) in the number by two. If the result is a two digit number, then add these digits together to make a single digit

4162 0012 3456 789a

9(2)+7(2)+5(2)+3(2)+1(2)+0(2)+6(2)+4(2)

(18)+(14)+(10)+(6)+(2)+(0)+(12)+(8)

Remember that If the result is a two digit number, then add these digits together to make a single digit

so

(1+8)+(1+4)+(1+0)+(6)+(2)+(0)+(1+2)+(8)

(9)+(5)+(1)+(6)+(2)+(0)+(3)+(8)=34

step 2

add every odd-position digit

4162 00123456 789a

so

8+6+4+2+0+2+1=23

step 3

Adds the result in step 1 and the result in step 2

34+23=57

The check-digit is what number needs to be added to this total to make the next multiple of 10

In our case, we’d need to add 3 to make 60

therefore

The check number is 3

6 0

3 years ago

What was the population in 2008? Can someone explain this to me?

Bas_tet [7]

Answer:

UNITED STATES ITALY DEM. REP. CONGO

Population mid-2008 305 million 60 million 67 million

Population 2050 (projected) 438 million 62 million 189 million

Lifetime births per woman 2.1 1.3 6.5

Percent of population below age 15 20% 14% 47%

Percent of population ages 65+ 13% 20% 3%

Life expectancy at birth 78 years 81 years 53 years

Annual births 4.3 million 568,120 2.9 million

Annual deaths 2.4 million 575,300 0.8 million

Annual births minus deaths 1.9 million -7,200 2.1 million

Percent of population undernourished <2.5% <2.5% 74% hope this helps!

6 0

2 years ago

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The amount of attendance at a dinner must go from being 57 people to 65 people. What is the percent of change

cestrela7 [59]

Answer:

4%

Step-by-step explanation:

5 0

3 years ago

Scientific Notation

Katarina [22]

3.615 x 10^2 i hope this helps

3 0

2 years ago

Read 2 more answers