SOLUTION: Consider the functions {{{ f(x)= 3/x }}} and {{{ g(x)= 3/x }}}, find f(g(x)) and g(f(x)). Determine whether f and g are inverses of each other. I know both f and g are inverses

Algebra.Com
Question 1077061: Consider the functions and , find f(g(x)) and g(f(x)). Determine whether f and g are inverses of each other.
I know both f and g are inverses of each other as they're both x.
f(g(x)) = x
g(f(x)) = x
For both f(g(x)) and g(f(x)) what are values that should be excluded from the domains? Since they're both I thought it was either excluding 0 from the domain or no values should be excluded from the domain? I'm not sure.
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.
You correctly determined that both f and g are inverses of each other as their composition is x.


But it DOESN't mean that

f(g(x)) == x identically for all x.


It only means that f(g(x)) == x identically for all  x from the DOMAIN of g.



The domain for each of the function  f(x) =   and  g(x) =  is the set of all real numbers EXCLUDING x = 0.



RELATED QUESTIONS

consider the function f(x)=x^3-4 and g(x)=3 sqrt x+4 a. find f(g(x)) b. find g(f(x)) (answered by Theo)
Show work please. consider the functions f(x)=4x-16 and g(x)= x/4 +4. Find f(g(x)) and... (answered by josgarithmetic)
For each pair of functions f and g below, find f(g(x)) and g(f(x)). Then, determine... (answered by stanbon)
Find f(g(x)) and g(f(x)) and determine whether the functions f and g are inverses of each (answered by Fombitz)
Consider the function f(x)=3x-6 and g(x)=x/3+2. A) Find f(g(x)). B) Find g(f(x)). C)... (answered by ReadingBoosters)
f(x)=5x+4/x+6 and g(x)=6x-4/5-x (a) find f(g(x)) (b) find g(f(x)) (c) determine (answered by solver91311)
inverse functions find f(g(x)) and g(f(x)) and determine whether the functions f and g (answered by drk)
find f (g(x)) and g (f(x)) and determine whether each pair of functions f and g are... (answered by lwsshak3)
3. If f(x)=square root 2x^2-1 and g(x)=x^1/2, find (and simplify) a) (f+g)(x) b)... (answered by CPhill)