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Sub 505 (Easy)|   Algebra|      
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shakticnb
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If g(x) = x + 4 for all x and f(x) = (2x^2 - 5)/x for all nonzero x Updated on: 31 Aug 2015, 21:59
Originally posted by shakticnb on 31 Aug 2015, 14:23.
Last edited by Bunuel on 31 Aug 2015, 21:59, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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E
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89% (01:31) correct 11% (01:58) wrong based on 128 sessions

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If g(x) = x + 4 for all x and f(x) = (2x^2 - 5)/x for all nonzero x, then f(x) = g(x) for which of the following values of x ?

A. –5
B. –3
C. 1
D. 3
E. 5
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E
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If g(x) = x + 4 for all x and f(x) = (2x^2 - 5)/x for all nonzero x 31 Aug 2015, 21:24
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shakticnb
If g(x) = x + 4 for all x and f(x) =2x^2 -5/x
for all nonzero x, then f(x) = g(x) for which of
the following values of x ?

A. –5
B. –3
C. 1
D. 3
E. 5
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Please be very careful while typing the question. Ensure there is no ambiguity. Brackets are required around 2x^2 - 5 since otherwise no option will satisfy f(x) = g(x). x must divide the whole expression

\(g(x) = x + 4\)

\(f(x) = \frac{(2x^2 - 5)}{x}\)

Plug in x = 1 first.
\(g(x) = x + 4 = 5\)
\(f(x) = \frac{(2*1 - 5)}{1} = -3\)
Does not satisfy

Next, try 5. g(x) is an integer in every case. Numerator of f(x) will be divisible by 5 so f(x) will be an integer in case x = 5. Hence it makes sense to try 5 next.
\(g(x) = 5 + 4 = 9\)
\(f(x) = \frac{(2*5^2 - 5)}{5} = 9\)
Satisfies.

Answer (E)
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OptimusPrepJanielle
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If g(x) = x + 4 for all x and f(x) = (2x^2 - 5)/x for all nonzero x 31 Aug 2015, 20:28
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Hi shakticnb,

What is the source of the question?
None of the answers given here are correct.
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If g(x) = x + 4 for all x and f(x) = (2x^2 - 5)/x for all nonzero x 01 Sep 2015, 10:30
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x+4=\(\frac{(2x^2-5)}{x}\)
\(x^2+4x=2x^2-5\)
\(x^2-4x-5=0\)
(x-5)(x+1)=0
x=5 OR -1

Answer: E
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If g(x) = x + 4 for all x and f(x) = (2x^2 - 5)/x for all nonzero x 04 Sep 2016, 21:04
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Hi shakticnb,

This question can be solved by TESTing THE ANSWERS. We're told that one of the 5 answers, when 'plugged in' for X, will lead to the SAME result in the two given equations. Thus, we just have to do enough work to find the one value that does that.

You likely don't need me to do the basic arithmetic for you, but only one answer ends in the same result for the given equations:

Show Spoiler
E; X=5
g(5) = 5 + 4 = 9
f(5) = (50 - 5)/5 = 45/5 = 9

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If g(x) = x + 4 for all x and f(x) = (2x^2 - 5)/x for all nonzero x 28 Apr 2022, 11:54
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