1. ## couple Algebra questions

I have a couple of questions to ask on some algebra. I have an upcomming exam and i just wanted to see if you guys could help me out and explain how these are done. thank you very much.

1) Given f(x)= 3-x^2 find f(t-1)

i could not figure this out correctley, i kept on comming up with t^2-2t+1 but my proffesor says this is incorrect.

2) Given f(x)=1/(x+1) and g(x)=(x+1)/3x, what is (g o f)(x)?

ive had a lot of difficulty with these types of problems and can never figure them out.

3) Solve (4/5)n + 2= -3(3/4n -8)

I think my brain is going out because i have tried this problem at least 10 times and can't seem to get it right.

2. 1.) $f(t-1)=3-(t-1)^2=3-(t^2-2t+1)=-t^2+2t+2$

You're just getting mixed up with the signs by the looks of it.

2.) For these types of problems, just replace any ocurance of 'x' in g(x) with the function f(x)...i.e. you are 'composing g with f.' so for your example:

$g(x)=\frac{x+1}{3x}$
$g\circ f(x) = \frac{f(x)+1}{3f(x)} = \frac{\frac{1}{x+1}+1}{3\frac{1}{x+1}} = \frac{\frac{1}{x+1}}{\frac{3}{x+1}} + \frac{1}{\frac{3}{x+1}}$ $= \frac{1}{x+1}\frac{x+1}{3} +\frac{x+1}{3}= \frac{1}{3}+\frac{x+1}{3} = \frac{x+2}{3}$

3.) I can't finish this right now, but looks like you might have to complete the square.