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
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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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Gmat_mission
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STRATEGY: As with all GMAT Problem Solving questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?Gmat_mission wrote: ↑Sun Dec 12, 2021 6:43 amIf \(f(x)=x^2-9\) 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
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
