Composite function Question

[-Whiplash-]

Hi, I've been doing Pre-Calculus by Correspondence for a little while now, and after a while everything was going fine, but now I'm having trouble with the following composite Function question:

F(x) = (3x)/(x^2 + 3x + 2), g(x) =(5x)/(x+1)

simplified expression for (f•g)(x), I get about as far as f((5x)/(x+1))

so I write out: (3(5x)/(x+1))/( (5x)/(x+1)^2 + 3(5x)/(x+1)+2)



And then it confuses me, I’ve looked through my book and I can’t find an equation nearly as difficult as this. How would I go about solving this?

 

[Deleted member 4993]

Hi, I've been doing Pre-Calculus by Correspondence for a little while now, and after a while everything was going fine, but now I'm having trouble with the following composite Function question:

F(x) = (3x)/(x^2 + 3x + 2), g(x) =(5x)/(x+1)

simplified expression for (f•g)(x), I get about as far as f((5x)/(x+1))

so I write out: (3(5x)/(x+1))/( (5x)/(x+1)^2 + 3(5x)/(x+1)+2)



And then it confuses me, I’ve looked through my book and I can’t find an equation nearly as difficult as this. How would I go about solving this?

You don't solve it - you can simplify it:

\(\displaystyle \displaystyle{\dfrac{3*g(x)}{[g(x)]^2 +3*g(x)+2}}\)

\(\displaystyle g(x) = \dfrac{5x}{x+1} \)

\(\displaystyle \displaystyle{\dfrac{3*\dfrac{5x}{x+1}}{[\dfrac{5x}{x+1}]^2 +3*\dfrac{5x}{x+1}+2}}\)

\(\displaystyle \displaystyle{\dfrac{\dfrac{15x}{x+1}}{[\dfrac{25x^2}{(x+1)^2}] +\dfrac{15x(x+1)}{(x+1)^2}+2\dfrac{(x+1)^2}{(x+1)^2}}}\)

\(\displaystyle \displaystyle{\dfrac{{15x}*{(x+1)}}{25x^2 +15x(x+1)+2(x+1)^2}}\)

Now continue simplification.....

 

[-Whiplash-]

Yo don't solve it - you can simplify it:

\(\displaystyle \displaystyle{\dfrac{3*g(x)}{[g(x)]^2 +3*g(x)+2}}\)

Really, that's it, I just write it out? I don't need to factor and cancel stuff and all that

 

[Deleted member 4993]

Really, that's it, I just write it out? I don't need to factor and cancel stuff and all that

You do have to do that - check my expanded reply above.