Melody

\(7\sqrt[3]{x}=x+8\\ 343x=x^3+3*x^2*8+3*x^1*64+8^3\\ 343x=x^3+24x^2+192x+512\\ 0=x^3+24x^2-151x+512\\\)

1) I answered something similar today, have you bothered to look?

2) If you present your question properly more people are likely to respond.

3)  What have you tried for yourself?

Let f(x) = 3x - 8 and g(f(x)) = 2x^5 - 5x - 3. Find g(-5).

f(x)=-5

3x-8=-5

3x=3

x=1

g(-5)=g(f(1)) = (2*1^5)-(5*1) -3 = 2-5-3 = -6

my sisters and I all have 2 more sisters than brothers, which means I am a girl.

So that means there are 3 more girls in the family than boys.

there might be  5 girls and 2 boys   

there might be  6 girls and 3 boys  etc

each boy will have  4 more sisters and brothers.

As examples:

if there were  5 girls and 2 boys   Then each boy would have 1 brother and 5 sisters

there might be  6 girls and 3 boys     Then each boy would have 2 brothers and 6 sisters

\(y=log_{\frac{1}{3}}(\frac{\sqrt{27}}{3})\\~\\ y=log_{\frac{1}{3}}(\frac{\sqrt{3^3}}{3})\\~\\ y=log_{\frac{1}{3}}(\frac{3^{3/2}}{3^1})\\~\\ y=log_{\frac{1}{3}}(3^{1/2})\\~\\ y=log_{\frac{1}{3}}((\frac{1}{3})^{-1/2})\\~\\ y=\frac{-1}{2}log_{\frac{1}{3}}(\frac{1}{3})\\~\\ y=\frac{-1}{2}*1\\~\\ y=\frac{-1}{2}\\~\\\)

LaTex:

y=log_{\frac{1}{3}}(\frac{\sqrt{27}}{3})\\~\\
y=log_{\frac{1}{3}}(\frac{\sqrt{3^3}}{3})\\~\\
y=log_{\frac{1}{3}}(\frac{3^{3/2}}{3^1})\\~\\
y=log_{\frac{1}{3}}(3^{1/2})\\~\\
y=log_{\frac{1}{3}}(\frac{1}{3}^{-1/2})\\~\\
y=\frac{-1}{2}log_{\frac{1}{3}}(\frac{1}{3})\\~\\
y=\frac{-1}{2}*1\\~\\
y=\frac{-1}{2}\\~\\

ok thanks, I will look at it properly later on    

As I said, I am not ultra-confident with this topic but that sounds right to me. 

Why don't you become a member?

It is easier to track your posts.

Members do tend to get priority.

and it is easier to attract people's attention through private messaging. 

Plus it is completely free.  

I think you can also get email alerts when you get a question response too (although I am not certain on that point)

You could even make some good friends here.    I have 

He started with x books

(half of x) + 10 = 24

now work out x

I think that is too simplistic:

Consider this new example.

f(x)=3x   where   x>4

g(x)=x^2   where  x<-1

f(g(x))=3x^2

certainly  x must be less than -1

but

x^2 must also be bigger than 4 which means that  x>2 or  x<-2

The intersection of these two restrictions,  x<-1 and x<-2  is x<-2

so I believe that the domain of   f(g(x)) is   x<-2

I have answered on the original.