Composite functions: f=x-4, g=rad x-3, find f.g, g.f

[aewhite07]

Hello everyone I'm new. I'm doing composite functions and I' m alittle confused when the equation involve radicals. I need help! Here is the problem: If f(x)=x - 4 and g(x)= radicand x-3 Find (f.g)(x) and (g. f)(x).Now I totally understand that (f.g)(x)=f(g(x)). and i am to replace the occurences of x with g(x).

(f.g)(x)=f(g(x))=(g(x))^2-4
=(radicand x-3)-4
Now which way do I go from here?

 

[skeeter]

Re: Compsite functions

\(\displaystyle f(x) = x - 4\)

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


\(\displaystyle f[g(x)] = \sqrt{x-3} - 4\) ... leave it as is.

\(\displaystyle g[f(x)] = \sqrt{(x-4) - 3} = \sqrt{x-7}\)