All categories

3 years ago

What is the inverse of y = 16x^2 + 1

Mathematics

1 answer:

tankabanditka [31]3 years ago

4 0

X = 16y^2 + 1
x - 1 = 16y^2
(x - 1)/16 = y^ 2
( (x-1) / 16 ) ^1/2 = y
( (x-1) ^ 1/2 ) / 4 = y

You might be interested in

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

Tissues of living organisms consist primarily of organic compounds; that is, they contain carbon molecules known as proteins, ca

Marianna [84]

<span>A healthy human body is approximately 18% carbon, so to determine how many pounds of carbon a 200lb body contains, compute 200lbs X 0.18 = 36 pounds. To convert 36lbs to kilograms, multiply by the conversion factor 0.454. Therefore, 36lbs X 0.454 = 16.344 kg.</span>

6 0

3 years ago

Read 2 more answers

Which is an equation of the line through the origin and (3,4)? Please help

kondor19780726 [428]

B is the answers………..

8 0

2 years ago

How do you subtract 42 minutes from 1 hour ,25 minutes.explain what to do and why you do it?

aksik [14]

So 1 hour= 60 minutes
60+25= 85 minutes
Now we should subtract the 42
85-42=43

3 0

2 years ago

Shane wrapped the kite with paper. How many square inches of paper did Shane use to cover the front and back? 45 POINTS

arsen [322]

Answer:

576

Step-by-step explanation:

First off, we can use the area of a kite formula, (D1*D2)/2 to get the area of one side of the kite, which is simplified to 18 * 32 : which gets us 288. But because we are looking for the area of the front and back side, we multiply 288 by 2- getting the final answer of <u>576</u>.

7 0

2 years ago

Read 2 more answers