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Question 1012362: gog=g(g(x))
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! gog(x) = g(g(x)).
this is no different than fog(x) = f(g(x)), when the function called f is the exact same function as the function called g.
here's an example of gog(x).
let g(x) = x^2
gog(x) = g(g(x))
since g(x) = x^2, g(g(x)) becomes g(x^2).
since g(x) = x^2, then g(x^2) = (x^2)^2 = x^4.
when the argument is x, g(x) = x^2
when the argument is x^2 rather than x, you raplace x with x^2 to get g(x^2) = (x^2)^2.
let's do it with numbers to see if that's any clearer.
g(x) = x^2
let's find g(2).
g(2) = 2^2 = 4
gog(2) = g(g(2))
since g(2) = 4, then g(g(2)) = g(4) = 4^2 = 16.
the result from the inner function is passed to the outer function and then the outer function works on that.
bottom line:
gog(x) is the same as fog(x) when f performs the exact same function as g.
if f(x) = x^2 and g(x) = x^2, you would get exactly the same result from fog(x) as you would get from gog(x).
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