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

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

Is 499.50 great than or less than 499.05?

mote1985 [20]

Answer:

greater

Step-by-step explanation:

8 0

2 years ago

20 POINTS: solve for x.

lara [203]

Answer:x=7

Step-by-step explanation:

Here AD=6

AB=6 (tangents drawn from external point to a circle are equal)

Then BC=13-6=7

Now, CE=BC=7(tangents drawn from external point to a circle are equal)

EF=14-7=7

EF=FG=x=7(tangents drawn from external point to a circle are equal)

3 0

3 years ago

What is the circumference of the circle? (use 3.14 for pi)<br> r = 50mm

Alexxandr [17]

Answer:

Step-by-step explanation:

circumference = 2 $\pi$ r

= 2 × 3.14 × 50

= 31.4 mm

hope this helps

plz mark it as brainliest !!!!!!!!!!!

7 0

3 years ago