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If \(f(x)=x^2-9\) and \(g(x)=16x-73,\) for which of the following values does \(f(x)=g(x)?\)

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by Gmat_mission » Sun Dec 12, 2021 6:43 am
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If \(f(x)=x^2-9\) and \(g(x)=16x-73,\) for which of the following values does \(f(x)=g(x)?\)

A. -27

B. -8

C. 0

D. 8

E. 27

Answer: D

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Re: If \(f(x)=x^2-9\) and \(g(x)=16x-73,\) for which of the following values does \(f(x)=g(x)?\)

by Brent@GMATPrepNow » Mon Dec 13, 2021 7:16 am
Gmat_mission wrote: ↑
Sun Dec 12, 2021 6:43 am
 If \(f(x)=x^2-9\) and \(g(x)=16x-73,\) for which of the following values does \(f(x)=g(x)?\)

A. -27
B. -8
C. 0
D. 8
E. 27

Answer: D

Source: Veritas Prep
STRATEGY: As with all GMAT Problem Solving questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we can definitely test the answer choices.
Now we should give ourselves about 20 seconds to identify a faster approach.
We can also solve the question algebraically, and this may be faster than testing large x-values (such as x = 27).
So I'm going to solve the question algebraically

We want to find a value of x such that: f(x) = g(x)
Substitute to get: x² - 9 = 16x - 73
Since this is a quadratic equation, we must set it equal to zero.
Add 73 to both sides of the equation to get: x² + 64 = 16x
Subtract 16x from both sides: x² - 16x + 64 = 0
Factor: (x - 8)(x - 8) = 0
So, x = 8

Answer: D
Brent Hanneson - Creator of GMATPrepNow.com
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