Pre-Calc Query: Finding the Indicated Function Value

[MrTiger1991]

First off, thank you for taking the time to read my query. I realize you all likely have demanding schedules, and don't always have the time or energy to help everybody. My question is from my Pre-Calculus class, and I have absolutely no idea what I'm doing with these particular problems; I've asked my teacher for assistance repeatedly , but she has trouble explaining it to myself and several of my peers. The question is:

FInd the indicated function value of (f of g)(-2), given f(x) = 2 - x and g(x) = the square root of 3 - x.

I'd appreciate a step-by-step explanation of how to work these problems, because I'm sincerely confused. There are three more problems like the one listed above, the only difference being the value of the (f of g).
They are:

(f of g)(1)

(g of f)(1)

(g of g)(7)


Thank you again

 

[chrisr]

\(\displaystyle f\ o\ g(x)\ is\ f(g(x)).\)

\(\displaystyle First\ find\ g(x)\)

\(\displaystyle Is\ g(x)=\sqrt{3}-x\ or\ \sqrt{3-x}\ ?\)

\(\displaystyle Let's\ suppose\ it's\ \sqrt{3}-x.\)

\(\displaystyle g(x)=\sqrt{3}-x\)

\(\displaystyle f\ o\ g(x)=f(g(x))=f(\sqrt{3}-x)=2-(\sqrt{3}-x)=x+2-\sqrt{3}\)

\(\displaystyle If\ g(x)=\sqrt{3-x},\ then\ f(g(x))=2-\sqrt{3-x}\)

\(\displaystyle Now\ you\ only\ need\ place\ x=-2\ and\ x=1\ into\ the\ appropriate\ composite\ function.\)

\(\displaystyle g\ o\ f(x)\ is\ g(f(x))=g(2-x)=\sqrt{3-(2-x)}=\sqrt{1+x}\ or\ \sqrt{3}-(2-x)=\sqrt{3}+x-2.\)

\(\displaystyle Now\ place\ x=1\ into\ the\ appropriate\ one.\)