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Functions

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Functions

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If the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?

A. -4
B. -5
C. -6
D. -7
E. -9

OA is E

Can an Expert give a mathematical approach to solve this question? Thanks in advance.

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There are a number of ways we could solve this. The simplest approach would be to simply run a scenario on x=0 and note that the second term will always be higher unless x is very negative.

Alternatively, you could set both equations equal and solve for x. If 2x+4 = 3x+12 then x = -8 and that is the break even point. Numbers higher than -8 will have a max number 3x+12 whereas numbers below -9 will have a max number 2x+4.

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Elias Latour
Verbal Specialist @ ApexGMAT
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