Alright, so I got a review sheet for a math test, and as I was doing it, there were two problems I had no idea how to do.

Let f(x)=(5 + x)^2 and g(x)=a = squareroot(x). Determine the value of _a_ for f(x) and g(x) to be inverse functions.

The answer ends up being -5, but I can't figure out how to get that.

The other is:

Solve. squareroot(3x + 7) - 3 = squareroot(x + 2) This one comes out to 14.

If someone could scan in their work, or type it out, of how to do these, i would be eternally greatful.

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[This message has been edited by happydud (edited February 28, 2004).]

The negative 5 is the domain of the funtion (I think)

The second, you swuare both sides, bring the x over to one side, subtract 7, divide by 2, you get -3

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-3 is wrong fish.

And how is -5 the domain? I said in the problem that it was the value for a.
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MadQuack on Military school: Pro's: I get to shoot a gun. Con's: Everything else.
"I'm going to beat you until the laws of physics are violated!!" ! Maeve's Warcry

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[This message has been edited by happydud (edited February 28, 2004).]

1) in the f(x) equation, to make it an inverse, switch the x and y and solve for y, giving you y = sqrt(x) - 5. Thus giving you your -5 answer.

2) Square both sides, I guess.


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Answer to (2) is 14, use your calculator.

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[This message has been edited by lateralus (edited February 28, 2004).]

For the: squareroot(3x + 7) - 3 = squareroot(x + 2) one, I tried just squaring both sides. Here's my work:

squareroot(3x + 7) - 3 = squareroot(x + 2) square both sides
3x + 7 + 9 = x + 2 add the 7 and nine, then subtract 2 from both sides
3x + 14 = x subtract 14 from both sides, then subtract x from both sides
2x = 14 divide both sides by 2
x = 7.

Now, on the answer sheet she said x = 14..
So I guess maybe she just screwed up?

[edit- Lat: arrg. Well.. how do you get 14 mathematically? We can't just use a calculator on the test. :/]
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MadQuack on Military school: Pro's: I get to shoot a gun. Con's: Everything else.
"I'm going to beat you until the laws of physics are violated!!" ! Maeve's Warcry

RIP -MaDaVentor-. You will be missed.

[This message has been edited by happydud (edited February 28, 2004).]

[This message has been edited by happydud (edited February 28, 2004).]

3x + 7 - 6sqrt(3x+7) + 9 = x + 2 ............square both sides
3x - 6sqrt(3x+7) = x - 14 ..............subtract 16 from each side
-6sqrt(3x+7) = -2x - 14 ............subtract 3x
6sqrt(3x+7) = 2x + 14 ............multiply by -1
sqrt(3x+7) = 1/3x + 7/3 .............divide by 6
3x + 7 = 1/9x^2 + 14/9x + 49/9 ............square both sides again
0 = 1/9x^2 - 13/9x - 14/9 ........set equal to 0
0 = x^2 - 13x - 14 ........multiply by 9
0 = (x - 14)(x + 1) ......factor
x = 14 or x = -1 .......solve

Since you squared the function(twice even), you need to test both values into the original for extraneous roots. You'll see that -1 doesn't work, so the only solution is 14.

Since with -1 you'll get

sqrt(7 - 3) - 3 = sqrt(2 -1)
sqrt(4) - 3 = sqrt(1)
2 - 3 = 1
-1 = 1

So obviously that value is thrown out.

[This message has been edited by Darth (edited February 28, 2004).]

[This message has been edited by Darth (edited February 28, 2004).]

I'm completely lost as to what you did. How did you get x - 14 on the last line? Where did that -6 come from on the first line?

[edit- Thanks. Looking it over again. Still a bit confused as to where the -6 part of -6sqrt came from..
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"I'm going to beat you until the laws of physics are violated!!" ! Maeve's Warcry

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[This message has been edited by happydud (edited February 28, 2004).]

Ok, here's my work. (BTW, you need to use FOIL when squaring.

sqrt(3x+7) - 3 = sqrt(x+2)
3x+7-6sqrt(3x+7) + 9 = x+2
-6sqrt(3x+7) = -2x - 14
sqrt(3x+7) = (1/3)x + (7/3)
3x+7 = (1/9)(x^2 + 14x + 49)
27x + 63 = (x^2 + 14x + 49)
0 = x^2 - 13x - 14

x = 14

Dang it Darth!

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[This message has been edited by lateralus (edited February 28, 2004).]

I added in what I did.

That should explain it. What's said beside the function is what I did to the previous function to get the function on that line.

-6sqrt comes from -3sqrt - 3 sqrt

(sqrt(3x + 7) - 3)^2
(sqrt(3x + 7) - 3)(sqrt(3x + 7) - 3)

First terms : sqrt(3x + 7) * sqrt(3x + 7)
First and second: sqrt(3x + 7) * -3
Second and first: -3 * sqrt(3x + 7)
Last terms: 9

Combine all that and you get:
3x + 7 - 3sqrt(3x+7) - 3sqrt(3x+7) + 9
Combine them to get -6sqrt(3x+7)

[This message has been edited by Darth (edited February 28, 2004).]

It comes when you square the left side of the equation.



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Now your job is to find the volume of the solid of revolution created by that function when rotated around the x-axis on the interval [-2,14]...

[This message has been edited by Darth (edited February 28, 2004).]

42

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Math... Overload... *explodes*

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Even if you murdered or robbed, years wrong, but God loves;
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I like it

Im glad im done with Algebra.

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Pfft, simple calc. You can't scare me! I've taken linear algebra!!!!. Well, and nothing much else. Bio doesn't require all that much math. Maybe I'll go to BME, but that is later. Much later...


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I'm taking Chem I this year, and Physics next year. Not to mention precalc, calc AP, and all that good stuff. Hold me . Oh and happydud--we're taking a test on that crap monday. Going to be tons of fun ergh.

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LOL! You think that is difficult? Wait till Calc II in college.

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But Calc III is so wonderfully easier.

However, Non-Euclytian Math, I hear, is a *****.

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Isn't that where you can have parallel lines intersect each other?
<3 Euclid

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Oh, yes. So I hear.

Note: I'm going to stay as far away from that class as is humanly possible.

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"LC Tusken: the idiot is the person who follows the idiot and your not following me your insulting me your following the path of a idiot so that makes you the idiot"
NMGOH || Jack Chick preaches it