composition of functions

[KJF]

f(x)= 3x+ (x/sqrt(1+x^2)
g(x)= tan(x)-7x

(f o g)(x)=?

so far I figure that
(f o g)(x)=
f(g(x))
3(tan(x)-7x)+((tan(x)-7x)/(sqrt(1+tan(x)-7x)^2)
3tanx-21x+((tan(x)-7x)/sqrt(tanx^2-14tanx^2+49x+1)

Not sure if this is done, I am feeling overwhelmed, if anybody has any advice I'd really appreciate it.
Sorry for not using better math symbols, I don't know how. If anybody needs clarification, I'd be glad to explain.
Thanks, KJF

 

[lookagain]

f(x)= 3x+ >>(x/sqrt(1+x^2) \(\displaystyle \ \ \ \ \ \ \) Drop this parenthesis. For one thing, it doesn't have its match.



g(x)= tan(x)-7x




(f o g)(x)=?

so far I figure that



(f o g)(x)=



f(g(x))



3(tan(x)-7x)+((tan(x)-7x)/(sqrt(1+tan(x)-7x)^2)\(\displaystyle \ \ \ \ \)The quantity (tan(x) - 7x) is being squared, not (1 + tan(x) - 7x).



3tanx-21x+((tan(x)-7x)/sqrt(tanx^2-14tanx^2+49x+1) \(\displaystyle \ \ \ \ \ \ \)Don't expand the square of that binomial.




Not sure if this is done, I am feeling overwhelmed, if anybody has any advice I'd really appreciate it.
Sorry for not using better math symbols,...\(\displaystyle \ \ \ \ \ \) Maybe change them up and use square brackets and
braces in addition to parentheses. Also, for more readability, use more horizontal spacing between
characters and vertical spacing between lines.

I would leave it like this:


3[tan(x) - 7x] + [tan(x) - 7x]/sqrt{1 + [tan(x) - 7x]^2}



Or, in Latex, I would leave it like this:



\(\displaystyle 3[tan(x) - 7x] \ \ + \ \dfrac{tan(x) \ - 7x}{\sqrt{1 \ + \ [tan(x) \ - \ 7x]^2 \ }}\)

 

[KJF]

Thank you! That was actually the first thing I wrote in my notebook, guess I was over-thinking things.