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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

Best Answer 

 #1
avatar+2551 
+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
avatar+2551 
+4
Best Answer

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
avatar+106533 
+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    !!!

 

 

 

cool cool cool

 Nov 7, 2019

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