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zalisa [80]
3 years ago
8

Find the inverse function for

Mathematics
1 answer:
kifflom [539]3 years ago
6 0
\bf \stackrel{f(x)}{y}=\sqrt{2x-6}\qquad \qquad \stackrel{f^{-1}(x)}{y}=\cfrac{x^2+6}{2}

that is correct hmmmm, yes, I think the restriction is also correct, it has to be x > 0, because, the domain on the original, has a restriction of x⩾3, otherwise the radicand turns negative.

now, the graph of that original function is a parabola sideways opening to the right, if you include both sides of the vertex of the parabola, it will not pass the vertical-line-test and not be a function, but if you restrict it to only positive roots, so it'll only be on the 1st quadrant, then it functions ok.

that means, the range of the original function, has to stick to only 0 or positive root values, now, recall that the range of the original is the domain of the inverse.  Therefore, the domain of the inverse, will have to stick to only 0 or positive values, since it's bound to the same restriction as the original's range.

notice the picture below of both, the dashed section is the positive range for each, if you include it, the original will fail the vertical-line-test, and the inverse will fail the horizontal-line-test.

recall that for a function to have an inverse, they both must pass the vertical and horizontal line test, or be a one-to-one functions.

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Translate the sentence into an inequality.
Luda [366]

Answer:

5 + c > -22

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

<u>Algebra I</u>

  • Inequalities

Step-by-step explanation:

<u>Step 1: Define</u>

Sum of 5 and c is greater than -22

↓ <em>Identify</em>

Sum = addition

  • 5 + c

Is greater than = inequality

  • >

Add them all together:

5 + c > -22

8 0
3 years ago
0.5 recurring as a fraction​
Klio2033 [76]

0.5 = 5/10 = 1/2

The answer is 1/2

5 0
2 years ago
Read 2 more answers
I need help pls
andre [41]

\large\bf{\underline{Given \: equations:}}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large \: x + 71 = 180

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large \: x + 149 = 180

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large \: x + 40 = 180

__________________________________________

\large\bf{\underline{On \: solving :}}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹x + 71 = 180

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹x = 180 - 71

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹x = 109

__________________________________________

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹x + 149 = 180

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹x = 180 - 149

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹x = 31

__________________________________________

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹x + 40 = 180

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹x = 180 - 40

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹x = 140

__________________________________________

4 0
2 years ago
Noah has d dollars to buy s songs from a website. The the website has an initial charge of $5 to join and then $0.99 for each so
Romashka [77]

Answer:

5 + 0.99s = d

Step-by-step explanation:

5 dollars is the initial price for the site and each song is 0.99, so if you multiply that by s, the number of songs, you'll get d.

3 0
3 years ago
Help me pls I kind of confused
Sunny_sXe [5.5K]
Ok so basically you have to anahajahabdbnxnxkskalakand
4 0
2 years ago
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