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

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Joined: 02 Sep 2009
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If f(x) = 2x - 2 and g(x) = 4 - x, then f(g(x)) = g(f(x)) for which of  [#permalink]

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23 Jun 2020, 02:55
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35% (medium)

Question Stats:

73% (01:53) correct 27% (01:16) wrong based on 26 sessions

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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

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Re: If f(x) = 2x - 2 and g(x) = 4 - x, then f(g(x)) = g(f(x)) for which of  [#permalink]

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23 Jun 2020, 04:11
1
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.
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Re: If f(x) = 2x - 2 and g(x) = 4 - x, then f(g(x)) = g(f(x)) for which of  [#permalink]

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23 Jun 2020, 04:16
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
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Re: If f(x) = 2x - 2 and g(x) = 4 - x, then f(g(x)) = g(f(x)) for which of  [#permalink]

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23 Jun 2020, 05:04
1
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))

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Re: If f(x) = 2x - 2 and g(x) = 4 - x, then f(g(x)) = g(f(x)) for which of   [#permalink] 23 Jun 2020, 05:04