If f (x) = x + 2 and g (x) = x^2, then for what value of x does f(g(x)) = g(f(x))? Express your answer as a common fraction.

literally substitute

\(f(x)=x+2\)

\(g(x)=x^2\)

So first find \(f(g(x))\)

That is \(f(x^2)\)

Then find \(g(f(x))\)

That is \(g(x+2)\).

So now we have \(f(x^2)=g(x+2)\)

Ok now solve

I am not educated on these type of functions, so when I personally solved it, I got:

x^2+2=(x+2)^2 = x=-((1/2))

\(\boxed{x=-\frac{1}{2}}\)

I am not sure someone please check my calculations!

We want to find out where

(x^2) + 2   =  (x + 2)^2          simplify

x^2  + 2   =  x^2  + 4x  +  4

2  =  4x + 4

- 2  =  4x

-1  =  2x

x  = - 1/2

Just as CU  found    !!!