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f(x) = and g(x) = 3x – 2. If f(g(x)) = 1, what is the value

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GMAT Club Legend
GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1653 [0], given: 396

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f(x) = and g(x) = 3x – 2. If f(g(x)) = 1, what is the value [#permalink] New post 27 Jul 2018, 07:07
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00:00

Question Stats:

42% (00:07) correct 57% (01:36) wrong based on 7 sessions
\(f(x) = \frac{2-x}{5}\)and \(g(x) = 3x - 2\). If \(f(g(x)) = 1\), what is the value of x?

(A) \(\frac{-5}{3}\)
(B) \(\frac{-1}{3}\)
(C) \(\frac{2}{3}\)
(D) 1
(E) \(\frac{5}{3}\)
[Reveal] Spoiler: OA

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Sandy
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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1653 [0], given: 396

CAT Tests
Re: f(x) = and g(x) = 3x – 2. If f(g(x)) = 1, what is the value [#permalink] New post 12 Aug 2018, 05:11
Expert's post
Explanation

Substitute the expression for g(x) into the function for f(x), and set the answer equal to 1.

Since g(x) = 3x – 2, substitute the expression 3x – 2 in for x in the expression for f(x):

\(f(g(x))=\frac{2-g(x)}{5}=\frac{2-(3x-2)}{5}=\frac{4-3x}{5}\).

Since f(g(x)) = 1, solve the equation \(\frac{4-3x}{5}= 1\):

\(4 - 3x = 5\)

\(-3x = 1\)

\(x = -\frac{1}{3}\)
_________________

Sandy
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Re: f(x) = and g(x) = 3x – 2. If f(g(x)) = 1, what is the value   [#permalink] 12 Aug 2018, 05:11
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f(x) = and g(x) = 3x – 2. If f(g(x)) = 1, what is the value

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