If f(x) = 2x - 2 and g(x) = 4 - x, then f(g(x)) = g(f(x)) for which of

Question

If  f(x) = 2x- 2  and  g(x) = 4 - x , then  f(g(x)) = g(f(x))  for which of the following x values?

I. -2
II. 0
III. 2

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

IanStewart · Answer

By substitution,

f(g(x)) = f(4-x) = 2(4 - x) - 2 = 6 - 2x

and

g(f(x)) = g(2x - 2) = 4 - (2x - 2) = 6 - 2x

so f(g(x)) and g(f(x)) are identical no matter what x is equal to.

mSKR · Answer

fgx means = 2( 4-x) -2= 8-2x-2= 6-2x
gfx means = 4-(2x-2)= 4-2x+2= 6-2x

as both are same factors 
then any value of x should result in fgx = gfx

hence option E

yashikaaggarwal · Answer

F(x) = 2x-2
G(x) = 4-x

F(G(x)) = G(F(x))
F(4-x) = G(2x-2)
2(4-x)-2 = 4-2x+2
8-2x-2 = 6-2x
6-2x = 6-2x

So, irrespective of any value, integer or not. F(G(x)) will always be equal to G(F(x))

Answer is E

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BrushMyQuant · Answer

f(x) = 2x- 2  and  g(x) = 4 - x  and  f(g(x)) = g(f(x))

Let's find the value of  f(g(x))

f(g(x)) = f(4-x)  
= 2*(4-x) - 2   
= 8 - 2x - 2 = 6 - 2x

Let's find the value of  g(f(x))  
g(f(x) = g(2x - 2)  
= 4 - (2x-2)  
= 4 - 2x + 2 = 6 - 2x

So,  f(g(x)) = g(f(x))  for all values of x
=> all values are possible -2,0,2

So,  Answer will be E 
Hope it helps!

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