Melody

I think that this question was answered in the last couple of days already. (By someone else)

BUT

y=3-x  This is a line with gradiene = -1 so when it is reflected across y=x it stays the same

So its inverse is y=3-x

$$f(0)=3\qquad so \qquad f^{-1}(0)=3$$    

$$\\y=-x^3+2x^2+3x\\
inverse\;\; function\\
x=-y^3+2y^2+3y\\
when\;\; x=6\\
6=-y^3+2y^2+3y\\
0=-y^3+2y^2+3y-6\\
0=-y^2(y-2)+3(y-2)\\
0=(-y^2+3)(y-2)\\
3-y^2=0\qquad or \qquad y-2=0\\
y^2=3\qquad \qquad or \qquad y=2\\
y=\pm\sqrt{3}\qquad \qquad or \qquad y=2\\
y=\pm1.732 \qquad \qquad or \qquad y=2\\
but\;\; y>3 \\
$So no solutions to $ f^{-1}(6)$$

NO SOLUTION.

I have replace the graph the original one had the wrong coefficients and caused me great confusion.

We should call ourselves the "Dazed and Confused" forum      

4/4+4/4+4/4+4/4+4/4+4/4+4/4+4/4+4/4+4/4=10

In maths it is called factorial

6 factorial = 6! = 1*2*3*4*5*6 

$${\mathtt{6}}{!} = {\mathtt{720}}$$

It is heavily used in probabability   

$$\\-3=2x^2-5x\\
0=2x^2-5x+3\\
$multiply to 6, add to -5 numbers are -2 and -3$\\
$change -5x into -2x-3x$\\
0=2x^2-2x-3x+3\\
0=2x(x-1)-3(x-1)\\
0=(2x-3)(x-1)\\
2x-3=0 \qquad or \qquad x-1=0\\
x=3/2\qquad \quad or \qquad x=1\\$$

Because I am not even ??

Hi again

I'm on my phone so it is a bit hard to see properly.  Looks good though.  Do you fully understand?

I Found it easiet to use neg indices rather than do everything as fractions but it makes no difference.

When I said write a new post I did not mean to start a new thread.  I just meant a new post on the original thread.  LOL  :)

Sorry - I did not ralise that you had answered.

It is better to put it in a new post so that it can be seen.

YES   that is exactly what I mean :)

Also, this is how you do the limit in LaTex

\displaystyle \lim_{x\rightarrow \infty}

$$\displaystyle \lim_{x\rightarrow \infty}$$

-0.994 that is half way between

Well some are more than a half and some a less.  do you can cross off the ones that are less that or equal to 1/2

That does not leave many.  (Only 2)

One of those is really close to 1/2  the other is larger.  See if you can do a bit more by yourself now.

Can you tell me which ones are bigger than 1/2 ?