Thread: combined functions

I am having a terrible time with this combined function.

f(x)= 2x-1/x+3 and g(x)=3x+1/-x+2

f(g(x))=?

I don't remember much from Algebra 1 and 2 in highschool, it was ten years ago and I'm sure I covered this there. Now I'm wishing I'd taken college algebra before enrolling in precalc.

Help?

Thank you,
Jonah Lefholtz

Originally Posted by jlefholtz

I am having a terrible time with this combined function.

f(x)= 2x-1/x+3 and g(x)=3x+1/-x+2

f(g(x))=?

I don't remember much from Algebra 1 and 2 in highschool, it was ten years ago and I'm sure I covered this there. Now I'm wishing I'd taken college algebra before enrolling in precalc.

Help?

$\displaystyle fg(x)=f[\frac{3x+1}{-x+2}]$

$\displaystyle =\frac{2(\frac{3x+1}{-x+2})-1}{\frac{3x+1}{-x+2}+3}$

Originally Posted by jlefholtz

f(x)= 2x-1/x+3 and g(x)=3x+1/-x+2

f(g(x))=?

I don't remember much from Algebra 1 and 2 in highschool...

To refresh your memory, try these lessons on function composition and simplifying "complex" fractions.

Originally Posted by mathaddict

$\displaystyle fg(x)=f[\frac{3x+1}{-x+2}]$

$\displaystyle =\frac{2(\frac{3x+1}{-x+2})-1}{\frac{3x+1}{-x+2}+3}$

Okay, that's as far as I got. It doesn't simplify any more? The solution my professor gave us says the answer to the function is "x" however, I couldn't derive it.

Thank you.

Originally Posted by jlefholtz

Okay, that's as far as I got. It doesn't simplify any more? The solution my professor gave us says the answer to the function is "x" however, I couldn't derive it.

Thank you.

Oh no , i stopped there to just let you continue .

Well , continue simplifying :

$\displaystyle \frac{\frac{6x+2+x-2}{-x+2}}{\frac{3x+1-3x+6}{-x+2}}$

$\displaystyle =\frac{7x}{7}$

$\displaystyle
=x
$

Ok. Thanks again. I keep getting 7x-3/7 so I'm close...I just need to figure out what I'm doing wrong. Thanks!