TonyDrummer2

There does not seem to be any link there haha

Nice!

Now I get it!

Thanks a lot!

You have any idea how one would find Ima f(x) ?

But that's exactly what I don't get.

If you set x=0 wouldn't that mean:

0=0(-0+6)   ?  cause that's = 0

I don't get how you can end up with x=6

Like how did you go from 0=x(-x+6) to 0= -x + 6

I don't understand this part:

x(-x+6)=0

Setting both factors to 0? Does that mean :

x=0

0(-0+6)=0

0=0

and then 

x=6

6(-6+6)=0

-36+36=0

(gives coords x=0 y=0 too)

By the way huge thanks for the help!

I just don't get the -16, +16 and the -9, +9 ...

Original answer by geno3141:

f(x)  =  4 - sqrt(16 + 6x - x2)

For ease of calculation, I am replacing  f(x)  with  y:

                                                                  y  =  4 - sqrt(16 + 6x - x2)

Subtract 4 from both sides:                  y - 4  =  - sqrt(16 + 6x - x2)

Multiply both sides by -1:                    -y + 4  =  sqrt(16 + 6x - x2)

Simplify left side:                                   4 - y  =  sqrt(16 + 6x - x2)

Square both sides:                            (4 - y)2  =  16 + 6x - x2

Multiply out:                                16 - 8y + y2  =  16 + 6x - x2

Subtract 16 from both sides:           - 8y + y2  =  6x - x2

Rewrite:                                              y2 - 8y  =  -x2 + 6x

Factor:                                                y2 - 8y  =  -(x2 - 6x)

Complete the squares:    [ y2 - 8y + 16 ] - 16  =  [ -(x2 - 6x + 9) ] + 9

Simplify:                                   [ y2 - 8y + 16 ] =  [ -(x2 - 6x + 9) ] + 25

Factor:                                               (y + 4)2  =  -(x - 3)2 + 25

Rewrite:                              (x - 3)2 + (y + 4)2  =  25  

Analysis:  this is the equation of a circle with center  (3, -4)  and  radius = 5.

But:  the initial equation is only the lower half of this circle; thus, an arc from  (-2,4)  through  (3,-1)  to  8,4).

log4(5x)=log4(x+1)

remove both "log4" terms

5x=x+1

5x-x=1

4x=1

x=1/4 or 0.25

x=6

84=10(6)  - 18y

18y = 10(6) -84

18y = 60 - 84

18y = -24

y= -24/18 or -1,33333....

1.5/4 + 1.5/4 = 3/4 

Thanks a lot for your help!

Could you explain to me that "complete the squares" part?

I don't get why there's suddenly a +16 and -16 on one side and a two time +9 on the other.

Thanks!