geno3141

f(x)  =  x^(3/2) - 1

y  =  x^(3/2) - 1

Step #1:  interchange x and y:

          x  =  y^(3/2) -1

Step #2:  solve for y:

          x+ 1  =  y^(3/2)

          Square both sides:  (x + 1)^2  =  y^3

          Find the cube root of both sides:  (x + 1) ^(2/3)  =  y

Answer:  y  =  (x + 1) ^(2/3) 

If you have any questions, please post back.

x² + 4  =  0

x²  =  -4

If you have only real numbers, there will be no solution, but if you have complex numbers:

x  =  ±√-4

x  =  ±√4·√-1       where  √4 = 2  and  √-1  can be replaced with the symbol  i

x  =  ±2i

If there are two parts to a polynomial, A and B, 

and, if you know one part, part A,

and if you know the sum of the two parts, Sum,

since  A + B  =  Sum,

the part that you don't know, B, can be found by Sum - A.

Post back a specific problem and we can help you with that.

√32  =  √16·√2  =  4√2

4√2 + √2  =  5√2

(5√2)²  =  (5√2)·(5√2)  =  (5·5)·(√2)·(√2)  =  25·2  =  50

The calculator at ths site will be able to calculate this for you.

To find sin(2A):

Use formula:  sin(2A) = 2sin(A)cos(A).

Draw the diagram in the third quadrant.

Since the tan(A) = 1/3, the '1' represents the y-value and the '3' represents the x-value; but, since the angle ends in the third quadrant, both the x-value and the y-value are negative.

Using the Pytagorean theorem, the hypotenuse has value √10.

Thus, sin(A) = -1/√10   and  cos(A) has value -3/√10.

sin(2A) = 2(-1/√10)(-3/√10)  = 6/10.

No, because ...

For every division problem, there is a corresponding multiplication problem.

Example:  6 ÷ 2  =  3  because  2 x 3  =  6.

Example:  27 ÷ -3  =  -9  because  -3 x -9  =  27.

However, try  10 ÷ 0  =  ?  To get an answer to this problem, there must be a number so that 0 x that number  =  10. There isn't a number that works.

One strange case:  what is  0 ÷ 0  =  ?. This is different, because you can replace the question mark with every number:  0 x 0  =  0, 0 x 1  =  0, 0 x 2  =  0, etc. There is no answer in this case because every number works.  

One way to calculate this: Find the points that make this equation true:  -(7c - 18)(2c) = 0

                                           -(7c - 18)(2c) = 0

Divide both sides by -1:       (7c - 18)(2c) = 0

Either          7c - 18  =  0         or         2c  =  0

                           7c  =  18                     c  =  0

                             c  =  18/7

These two points separate the number line into three sections:

      the section where  c  <  0,  

      the section where  0 <  c  < 18/7,

      the section where  c  >  18/7

Try a number from the section where  c  <  0; try any negative number (I'll pick -2) in the original problem:      -(7c - 18)(2c) > 0     --->     -(7·-2 - 18)(2·-2)  =  -7(-32)(-4) > 0    this doesn't work!

Try a number from the section 0 <  c  < 18/7; I'll pick 1.                                                                                      -(7c - 18)(2c) > 0     --->     -(7·1 - 18)(2·1)  =  -7(-11)(2) > 0    this works!

Try a number from the section where  c  >  18/7; I'll pick 10.                                                                              -(7c - 18)(2c) > 0     --->     -(7·10 - 18)(2·10)  =  -7(52)(20) > 0    this doesn't work!

So the solution is  0 < c < 18/7.

(If there had been a  ≥  or a  ≤  sign in the original problem, there would be this type of sign in the answer.

3x - 2  =  10 - 2x

Add  2x  to both sides:         5x - 2  =  10

Add  2  to both sides:                5x  =  12

Divide both sides by 5:                x  =  12/5            

Because    (-2)² = 4     (-1)² = 1     (0)² = 0     (1)² = 1   

one possible function is  y = x².