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y  =  -9.16x^2 + 73.04x  + 183.3

Generated here :   http://keisan.casio.com/exec/system/14059932254941

2.

y  =  7x^2 - 3

y + 3  =  7x^2

[ y + 3 ] / 7   =  x^2

±√  [ (y + 3) / 7 ]  =  x

±√ [ ( x + 3) / 7 ]  ⇒    inverse

1.   Both will be functions.....no single "x" will have two different "y's"  associated with it.....it is "one-to-one"

And a "one-to-one" function's inverse will also be a function, i.e, "one-to-one"

The second answer is the correct one

thanks for commenting

3)

y  =  -4x^2  - 2      add 2 to both sides

y + 2  =  - 4x^2     divide both sides by  -4

[ y + 2 ] / -4  =  x^2

[ - y - 2 ]  / 4   =  x^2      take both roots

±√ [ - y - 2 ] / 2    =  x        swap, x , y      

±√ [ -x - 2 ]  / 2   =  y          and this is the inverse

Here's the graph of both :

https://www.desmos.com/calculator/sdlfeedlri

I really appreciate these posts Foxy :D

5)....This is kind of a "trick" question, NSS...it's not as tough as it appears

( g^-1  o  g) (4)    means     the same as    g^-1 (g(4) )

So   

g(4)  means that we are putting  4  into the function  and evaluating

So we have    14 / [ 4 + 3 ]   =   14/7   =  2

Now   we    have   

g^-1 (g(4)  =  g^-1(2)

Note that the  inverse  REVERSES the original coordinates...so....4  led us to 2  in the original function... (4,2).......so.......2  in the inverse leads us back to 4.....(2,4) !!!

So   g^-1 ( 2 )  =  4

4)

Let's write this as

y  = ( 7 - 8x)^2

The idea is to get  by itself  and then "swap"  x  and y

Take the square root of both sides

±√y  =  7-  8x              subtract  7 from both sides

-7 ±√y  =  - 8x             divide both sides by  -8   [ this has no affect on the  " ± " ]

[ 7 ±√y ] 8  =  x           "swap"  x and y

[ 7 ±√x ] / 8  =  y        for y, write   f^-1(x)

f^-1(x)   =  [ 7 ±√x ] / 8 

This is not a function.....to see why, ..let x  = 9

Note that we get 2 different  y values here.....(9, 5/4)   and (9, 1/2)

For something to be a function, we CANNOT have two different y values for the same x value !!!

So....the first answer is correct

Here's the graph :  https://www.desmos.com/calculator/470f3qvli7

NSS.... this graph DOES NOT pass the "vertical line" test......if we can draw a vertical line that cuts the graph more than once at any point, we do not have a function

(3)

f(x)  =  [ x^2  - 49]  / [ x + 7]         factor  the denominator

f(x)  =   [   ( x + 7) ( x - 7) ]  / ( x + 7)        this simplifies to

f(x)  =  x - 7

This is a line with a y intercept at  -7

Also......  x  = -7    will make the original denominator  0, so this is will the "hole" will occur

So.....the first graph is correct

(2)  

f(x)  =   3 / [ x - 2 ]  + 9

The function will be undefined when x  = 2  [ it makes a denominator = 0]

Also...... we have a lower power polynomial over a higher power polynomial in the first fraction..... like the first problem, this sets up a horiontal asymptote at y  = 0

However, the appended  "9"  shifts this asymptote up 9 units

So....we will have a horizontal asymptote at y  = 9

Here's a graph to confirm our suspicions :  https://www.desmos.com/calculator/p9km2zdfff

(1)   f(x)  =  3 / [5x^5]

If x = 0, the denominator is undefined.....so....the function is defined at all values except at x = 0

So....the domain  is    (-inf, 0), U (0, inf)

We have   a lower power polynomial in the numerator than in the denominator.....in a Lower/Higher situation, a rational function like this will always have a horizontal asymptote at y  = 0

Also....because the power on the variable in the denominator is odd, the function will generate both negative and positve values  in infinite directions both ways

So.....the range is     (-inf, 0) U   (0, inf)

Here's a graph to check this  : https://www.desmos.com/calculator/4s1yykzw1v

Slope  

Subtract the y coordinates in some order

7 - 2   =   5         (1)

Subtract the x coordinates in the same order

8 - 10   =   -2         (2)

Put    (1)  over (2)

5 / - 2    =

-5 / 2

your welcome i know it can get hard sometimes and it helps so that why i post 

Slope = rise/run = (y1-y2) / (x1-x2)  = (2-7) / (10-8) = (-5)/2 = -5/2

Thanks Man for the encouragement!!

Very nice, hectictar.....!!!

have yeal read a parragh about Ancient Greece. 

if yeal get this just tell me.

find the quotion.

6x4x60x68x45+45x23+34x34x5x67x78x90x98=

It works like this: Take a smaller number such as 10!. I hope you know what 10!(ten factorial) means. It means this: 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 =3,628,800. Notice that 2, 3, 4, 5, 6, 7, 8, 9, 10 are ALL factors of their product of 3,628,800. This means that 3,628,800 will divide any one these factors EVENLY. So, for example, 3,628,800 / 7 =518,400. OK?. Now, if you add another 7 to 10!, you will have:3,628,800 + 7 =3,628,807. Now, if you divide this new number by 7, you will get the following:

3,628,807 / 7 =518,401.... So, now you can see 10!+7 will divide 7 EVENLY again, and the original quotient of 518,400 is gone up to 518,401. And the 1 at the end of 518,401 simply means we have 1 extra 7 because we deliberately added to 10!. And this applies to all numbers from 2 to 10 when added to 10!. I hope this is clearer now.

sorry i get the varying part ...just other is confusing....its me rosala...i was just too lazy to log in....lol