SOLUTION: gog=g(g(x))

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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