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f(x) = and g(x) = 3x – 2. If f(g(x)) = 1, what is the value
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27 Jul 2018, 07:07
27 Jul 2018, 07:07
Expert Reply
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Question Stats:
75% (00:46) correct
24% (01:27) wrong based on 41 sessions
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\(f(x) = \frac{2-x}{5}\)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) \(\frac{5}{3}\)
(A) \(\frac{-5}{3}\)
(B) \(\frac{-1}{3}\)
(C) \(\frac{2}{3}\)
(D) 1
(E) \(\frac{5}{3}\)
Re: f(x) = and g(x) = 3x – 2. If f(g(x)) = 1, what is the value
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12 Aug 2018, 05:11
12 Aug 2018, 05:11
Expert Reply
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 \(\frac{4-3x}{5}= 1\):
\(4 - 3x = 5\)
\(-3x = 1\)
\(x = -\frac{1}{3}\)
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 \(\frac{4-3x}{5}= 1\):
\(4 - 3x = 5\)
\(-3x = 1\)
\(x = -\frac{1}{3}\)
gmatclubot
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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