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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

What would a piece 430 feet 3 inches cost if you get a 10% discount for the larger volume? A piece of wire cable 180 ½ feet long

alexgriva [62]

To get the answer to this question you would have to multiply these numbers.
The normal price appears to be 65.95 for 180.5 feet.
First we could divide 430.25 by 180.5
This divides out to become 2.39027778.
We would then multiply This by our normal price for 180.5 feet, which is 65.95.
This gives us 157.63882.
We would next need to take the 10 percent off. The easiest way to do this is to multiply our price by .90
This would give us 141.484938.

3 0

3 years ago

Find a polynomial with a degree of 3 and zeros -3,3,5

Aliun [14]

Answer:

f(x) = x³ - 5x² - 9x + 45

Step-by-step explanation:

Given x = a, x = b are the zeros of a polynomial, then

(x - a), (x - b) are the factors and f(x) is the product of the factors.

Here the zeros are x = - 3, x = 3 and x = 5, thus

(x + 3), (x - 3) and (x - 5) are the factors and

f(x) = (x + 3)(x - 3)(x - 5) ← expand the first pair of factors using FOIL

= (x² - 9)(x - 5) ← distribute

= x³ - 5x² - 9x + 45

6 0

3 years ago

One box holds 16 crayons. Another box hold 24 crayons. Write a sentence using words that compares the crayons in the two boxes

goldenfox [79]

Box 1 has 8 less than the box with 24 in it.

6 0

3 years ago

Read 2 more answers

A national study reported that 75% of high school graduates pursue a college education immediately after graduation. A private h

Verdich [7]

Answer:

The % students going to higher education is 79.60 % which is higher than the reported value.

Step-by-step explanation:

According to national study report the students going to college for higher education = 75 %

Given that

156 of their 196 graduates last year went on to college.

% students going to higher education is

$(\frac{156}{196}) 100 = 79.60$

Thus the % students going to higher education is 79.60 % which is higher than the reported value.

4 0

3 years ago