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This is just an expression involving x, y and z.  What do you want to do with it?

If you want to factor it the result is: 3y(x + 2z - 3y)

I'll assume this is f(x,y) = y(x)*x + 1 + b  where b is a constant, y is a function of x and you want df/dx:

df/dx = y(x)*dx/dx + x*dy(x)/dx +d(1+b)/dx  → y(x) + x*dy(x)/dx

. 

Have a look at http://web2.0calc.com/questions/a-b-c#r1 where I've re-written the questions in easily readable text form. 

I'll rewrite the question:

Suppose the domain of f is (-1, 1)

a) Define the function g by g(x) = f(x+1)  What is the domain of g?

b) Define the function h by h(x) = f(x) + 1  What is the domain of h?

c) Define the function j by j(x) = f(1/x)  What is the domain of j?

d) Define the function k by k(x) = f(sqrt(x))  What is the domain of k?

e) Define the function L by L(x) = f( (x+1)/(x-1) )  What is the domain of L?

and I'll answer the first one:

a)  Minimum value of domain of f is -1, so x_min + 1 = -1, or x_min = -2

     Maximum value of domain of f is +1 so x_max + 1 = 1, or x_max = 0

    Hence domain of g is (-2, 0)

Now you try some of the others.

Here are the graphs:

I think this might be :

3.54 * 10⁵  * 6.3 * 10⁴        which we can reorder as  :

3.54 * 6.3 * 10⁵ * 10⁴    =

22.302 * 10⁹  =

2.2302 * 10¹⁰

too much...

nah, 

4 hours = 4*60 = 240 minutes every day

35% of 240 = 84minutes every day

there are 30 days in june 84*30 = 2520minutes in june

2520/60 = 42 hours of math study?

35% of 4 hours  = 1.4 hours

30 days in June * 1.4 hrs per day  = 42 hours   spent revising Math in June

6x + 8y   =  6788

x - y  = 510

Using the second equation,  we can rearrange it as  :  x - 510  = y

And substituting for y in the first equation, we have

6x + 8 [ x - 510]  = 6788   simplify

6x + 8x - 4080   = 6788 

14x - 4080  = 6788       add 6788 to each side

14x  = 10868        divide both sides by 14

x  =  5434/7

And y = 5434/7 - 510  =  [5434 - 3570] / 7  =  1864 / 7

\(3.54\times105+6.3\times104\)

\(371.7+6.3\times104\)

\(371.7+665.2\)

\(1026.9\)

\(1.0269\times{10}^{3}\)

I see no diagram  :(

See the solution here by a mathematician at Oxford University:

https://www.youtube.com/watch?v=w3Nzkae_TRU

624 - [624 x 1/6] =

624 - 104 =520- Litres of water left at the end of the day.

A negative times a negative is equal to a positive.

What don't you understand? 10^1/2 means you take the square root of 10=3.1622.......or 10^2.5 means you multiply 10 x 10 x sqrt(10), or 10^1/2.=316.22....etc.

 \({20}^{0.2134}\)

\({20}^{\frac{2,134}{10,000}}\)

\({20}^{\frac{1,067}{5,000}}\)

\(\sqrt[5,000]{{20}^{1067}}\)

sqrt[5,000{1.58126760396336420587886989624154146132466132628236029966329185958929952787496364759344049766747753511864904581497509305773288076082651153802354218703701960876185487716067469815989771673510325266593568498806832084814068346425541170795393246600905903391257856650280288712760480168148830103270568366129692393209146672729292800*10^801}

1.8951334669765444

Go to YouTube and type "How to solve the Rubick's Cube"

If this is how it is written:  1/ 6.28* sqrt {(40*10^-6)*(200*10^-12)}=?, then the answer should be:

=1.42425… × 10^-8

16th july.  :)

I assume you mean to put each formula in the form \(y=mx+b\)

a) \(y=\frac{2}{7}x-3\)

\(y=\frac{2}{7}x+(-3)\)

b) \(4.7y-0.03x=0.4\)

\(4.7y=0.4+0.03x\)

\(y=\frac{0.4+0.03x}{4.7}\)

\(y=\frac{0.03}{4.7}x+\frac{0.4}{4.7}\)

\(y=\frac{3}{470}x+\frac{4}{47}\)

c) \(6y=2-5x\)

\(y=\frac{2-5x}{6}\)

\(y=\frac{2}{6}-\frac{5}{6}x\)

\(y=-\frac{5}{6}x+\frac{2}{6}\)

Note on (b)  above.......I assumed that we were dealing with functions only in this problem......thus my answer that "no inverse exits"  should be amended to "no inverse function exists"  ...however.....

g(x)  = 4x^2 + 8x + 13   has an inverse, but, since the original function is not one-to-one, the "inverse" will not be a function .....the inverse can be derived as follows :

g = 4x^2 + 8x + 13          complete the square  on x

y - 13 + 4  = 4(x^2 + 2x + 1)

[y - 9] / 4  =  (x + 1) ^2         take plus/minus square root of both sides

±sqrt [ y - 9] / 2 = x + 1

±sqrt [ y - 9] / 2  - 1   =  x        "swap" x and y

±sqrt [ x - 9] / 2  - 1   =  y  =  g^-1 (x)

So.....g^-1 (25)   =   ±sqrt [25 - 9]/ 2 - 1   =  ±4/2 - 1   =  ±2 - 1   =   1    and  -3

So  g^-1(25)   returns two values......   1 and -3.......therefore.....it is not a function

Because they are all NEGATIVE numbers:

{-2 4/5, -2.68, -2 2/3} They are sorted from the least to greatest, because -5 is SMALLER than -2.

We have that :

y = k/x

5 = k/9       multiply both sides by 9

45  = k

So .....when x = -3 we have

y =45/(-3)   = -15