SOLUTION: if there a function g that satifies f o g = g o f = f for all funtions? If so, what is it?

Algebra.Com
Question 425516: if there a function g that satifies f o g = g o f = f for all funtions? If so, what is it?
Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
If g(f(x)) = f(x) for all x, we can conclude that g(x) leaves x unchanged, so g(x) = x.
RELATED QUESTIONS

for the given funtions f and g, find (a) (f o g)(4) (b)(f o g)(2) (c)(f o f)(1)... (answered by nik_consult)
I kind of understand how functions work but this is just confusing and I dont understand... (answered by Jk22)
Find (a) (f o g)(x) and the domain of f o g and (b) (g o f)(x) and the domain of g o f.... (answered by stanbon)
Find (g o f)(3) if g(x) = 3x and f(x) = x - 3 Need help solving, I see the formula, but (answered by nyc_function)
Can I please have your assistance? If f(x) = 1 and g(x) = x2, what is f o g? What is g o... (answered by jim_thompson5910)
Can I please have your assistance? If f(x) = 2x +1 and g(x) = x2, what is f o g? What is... (answered by Theo)
Let f(x)= 2x+3 and g(x^2) Determine the formula for (g o g o g....o g)(x) where there... (answered by Fombitz)
I don't understand the o thing. Does it mean multiply or what? and I don't totally... (answered by Fombitz)
Let C(x)=(1+x^2)^3. Find the functions f and g so that C(x)=(f o g)(x) is true for all... (answered by stanbon)