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# 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.

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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.

Nov 7, 2019

#1
+2850
+4

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!

Nov 7, 2019
edited by CalculatorUser  Nov 7, 2019

#1
+2850
+4

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!

CalculatorUser Nov 7, 2019
edited by CalculatorUser  Nov 7, 2019
#2
+109740
+1

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    !!!

Nov 7, 2019