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3.  f(x)  = 3x  + 2

Here's the way I learned it..... for  f(x), write "y".... get x by itself... "swap" x and y

 and for "y"  write f^-1(x)  [this notation represents the inverse ]

So we have

y  = 3x+ 2

y - 2  = 3x

[y - 2] / 3  = x        "swap"  x and y

[x - 2 ] / 3  = y

[x -2 ] / 3  = f^-1(x)

BTW....swapping x and y like you did in your first step is  OK, too.....!!

#4   looks good...!!!

Here's  the last two

f(x)  = x^2  + 8

y = x^2 + 8

y - 8  = x^2        take both roots

±√ [y -8] = x      swap  x and y

±√[ x - 8 ]  = y

±√[x - 8]  =  f^-1(x)

f(x)  = (x + 3)^2

y = (x + 3)^2      take both roots

±√y = x + 3

±√y  - 3   = x      swap x and y

±√x  - 3   = y

±√x  - 3  =  f^-1(x)

Thanks, CPhill!

Nice, tertre....!!!!!!

How many of the first 100 rows contain at least one even entry and no odd entries other than 1  ??

I'm not sure, but looking at the patterns in the triangle for the first 20 rows shows that evey 2ⁿ row [ for  n ≥ 1 ]  will only contain even entries  [except for the beginning and ending  "1" entries in these rows]

So....we should have  6   rows since   2⁶  = 64th row.....   but 2⁷   = 128th row

We calculate, first,  pi/3=3.14/3 which is around 1.04, so ceiling function of that equals 2.

Next, the square root of 45 is greater than 6(6^2=36), and less than 7(7^2=49). Since it is greater than 4, the answer is 6.

Lastly, 8^2/3=(2^3)^2/3=2^2=4, which equals 4, Floor of that equals 4.

So, the answer is 2+6+4=8+4=\(\boxed{12}\).

Got it! Thank you~

To  find the inverse  just  reverse the co-ordinates

So...for the first one, we have

(-3, 1), (3, - 2), (1, 5),  ( 4, 6)

It's a function as long as no two different y values are paired with the same x value

[ In other words...an x value cannot be paired with two different y's ]

This doesn't happen, so the inverse is a function

For the second, we have

(7, - 5), (-8, -6), (-2,1) , (3, 10)

No two different y's are paired with the same x value, so this is also a function

That is all I have to do? ouo there is no way it's that simple xD

Inverse function: Switch the x and y. First one: (1,-3), (-3,1)

(a) Permutations:  n!/(n-r)!

(b): Since the power is -1, we can rewrite the number as 1/that number, so \((13578)^{-1}=\frac{1}{13578}\) .

If this is what you mean by (a), then:

7324165 nPr 645231* 1234567  nPr 123456

=2.620 131 405 190 192 662 934 080 966 39 E+5,165,891

Thanks! Your correct!

Alright. Good luck!

Hmm... No clue :(

I've definitely heard of it. I'm gonna go check it out!

Ummmm. https://www.investopedia.com/simulator/ is a game where you can invest with virtual money for free. I dunno. Hope this helps.

I'll check that out later, in the mean time do you possibly have a stock exchange game or anything similar to stocks or money management? 

Thanks! 

Wait. Actually I have a good game for you. EVE Online is a game where you control a company, which can help develop real world management skills.

There  are  [ 15 * 16 ] / 2 =  15 * 8   = 120  elements in the first  15 rows of Pascal's Triangle

And there  are   14 * 2  + 1 = 29  "1s"  -   two "1s" on every row except for one on Row  "0"

So....the probability of choosing a "1"  is   29 / 120

Sorry I'm no help on that front.

Yea that's not what I'm looking for :(

Honestly, I'm not sure. Starcraft is an RPG but I'm not so sure about how educational it is.

 LOL!