FUNCTIONS

[texas07]

Express the function F(x)=1/?(x+?(x)).
f(x) =
g(x)=
h(x)

My professor told me I had to basically work backwards. But honestly, I am lost. I went to our school math tutor and she even couldn't help me. I really need help and would be greatly appreciated if someone could help me take on this problem.

 

[tkhunny]

Well, do it.

Maybe...

h(x) = sqrt(x)

f(x) = 1/x

Now what?

 

[texas07]

I did that just now. And set g(x) = sqrt (x) as well. I am trying to put it all together right now. Thanks

 

[tkhunny]

You must build F(x) and prove it, first. Here's one FUNNY way.

\(\displaystyle F(x) = f\left(h\left[h^{2}(x)+h(x)\right]\right)\)

I didn't use g(x), so maybe I didn't quite do the assignment.

Maybe that's it. g(x) = x^2

\(\displaystyle F(x) = f\left(h\left[g(h(x))+h(x)\right]\right)\)

There is NOT just one way to do it.

 

[texas07]

Yeah, to find f(x), g(x), and h(x) so that F=f(g(h(x)))

What do you think of:
f(x) = 1/x
g(x)= sqrt (x) +x
h(x)= sqrt (x)

or

f(x)1/x
g(x)=x^2+x
h(x)=sqrt (x)


I'M GOING TO NEED SOME SERIOUS TUTORING AS YOU CAN SEE.

 

[tkhunny]

No, no. Your last one is excellent. Not so much on the first one, though.

Look carefully at g(h(x)) = sqrt(sqrt(x)) + sqrt(x)

That's no good.