_______ requirements are courses that build knowledge and skills in a specific

Find the inverse function of f(x)= 1+squareroot of 1+2x

Svetllana [295]

Answer:

Therefore the inverse function of $f(x)=1+\sqrt{1+2x}$ is $\frac{x^2-2x}{2}$

Explanation:

We need to find the inverse of function $f(x)=1+\sqrt{1+2x}$

Function Inverse definition :

$\mathrm{If\:a\:function\:f\left(x\right)\:is\:mapping\:x\:to\:y,\:then\:the\:inverse\:functionof\:f\left(x\right)\:maps\:y\:back\:to\:x.}$

$y=1+\sqrt{1+2x}$ $\mathrm{Interchange\:the\:variables}\:x\:\mathrm{and}\:y$

$x=1+\sqrt{1+2y}$

$\mathrm{Solve}\:x=1+\sqrt{1+2y}\:\mathrm{for}\:y$

$\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}$

$1+\sqrt{1+2y}-1=x-1$

Simplify

$\sqrt{1+2y}=x-1$

$\mathrm{Square\:both\:sides}$

$\left(\sqrt{1+2y}\right)^2=\left(x-1\right)^2$

$\mathrm{Expand\:}\left(\sqrt{1+2y}\right)^2:\quad 1+2y$

$\mathrm{Expand\:}\left(x-1\right)^2:\quad x^2-2x+1$

$1+2y=x^2-2x+1$

$\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}$

$1+2y-1=x^2-2x+1-1$

$\mathrm{Simplify}$

$2y=x^2-2x$

$\mathrm{Divide\:both\:sides\:by\:}2$

$\frac{2y}{2}=\frac{x^2}{2}-\frac{2x}{2}$

$\mathrm{Simplify}$

$y=\frac{x^2-2x}{2}$

Therefore the inverse function of $f(x)=1+\sqrt{1+2x}$ is $\frac{x^2-2x}{2}$

4 0

2 years ago

What is the letter for the trash directory on windows 10?

myrzilka [38]

It's usually in C: drive.
<span>C:\$Recycle.Bin
</span>But if you have several drives, there are Recycle Bins each drive.

3 0

3 years ago

Read 2 more answers

Use the Date object and the Array object to determine and diplay information about the current date on your webpage. Your output

Mnenie [13.5K]

Answer:

var today = new Date();
var dateComp = [];
dateComp[0] = today.getDate();
dateComp[1] = today.getMonth();
dateComp[2] = today.getFullYear();
switch(dateComp[1]){
case 0:
console.log("Jan " + dateComp[0] + "," + dateComp[2])
break;
case 1:
console.log("Feb " + dateComp[0] + "," + dateComp[2])
break;
case 2:
console.log("Mar " + dateComp[0] + "," + dateComp[2])
break;
case 3:
console.log("Apr " + dateComp[0] + "," + dateComp[2])
break;
case 4:
console.log("May " + dateComp[0] + "," + dateComp[2])
break;
case 5:
console.log("Jun " + dateComp[0] + "," + dateComp[2])
break;
case 6:
console.log("Jul " + dateComp[0] + "," + dateComp[2])
break;
case 7:
console.log("Aug " + dateComp[0] + "," + dateComp[2])
break;
case 8:
console.log("Sept " + dateComp[0] + "," + dateComp[2])
break;
case 9:
console.log("Oct " + dateComp[0] + "," + dateComp[2])
break;
case 10:
console.log("Nov " + dateComp[0] + "," + dateComp[2])
break;
case 11:
console.log("Dec " + dateComp[0] + "," + dateComp[2])
break;
}

Explanation:

The solution code is written in JavaScript.

Firstly, create a Date object (Line 1). The date object will automatically capture the current date and time.

Next create an array dateComp to hold the day, month and year (Line 3 -5). We use the getDate method to get current day, getMonth method for current month and getFullYear method for current year.

This is important to note that the getMonth method will return the value range from 0 - 11 with the Jan is represented as 0, Feb is 1 and so forth. Presume we intend to display the date using the format "month day, year", we can create a switch structure to check the month value which is range from 0 to 11. If month value is 0, generate string Jan + current day + "," + current year. We generate the date string based on different switch cases (7 - 44). We shall see the output similar to the date string as shown below:

Apr 12,2020

6 0

3 years ago

What can you use to make sure that you have no errors in Word Online?

Free_Kalibri [48]

Answer:

You can use grammarly. It woks amazingly!

Explanation:

3 0

2 years ago

What can you search on Microsoft Word or Powerpoint Clipart or Google (Clip art) to find more pictures like the ones below but w

elena-14-01-66 [18.8K]

Well if you put sad/mad/scared/tired/ect it should pop up with the same person.

3 0

3 years ago