# Practice GMAT Problem Solving Question

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f(x) = ; f(-1)=

Correct Answer:

**A**- To determine f(-1), we must first know (-1)
^{59}, (-1)^{57}, and (-1)^{56}. You should never multiply out hundreds of numbers. - Instead, look for a pattern:

(-1)^{1}=-1

(-1)^{2}=+1

(-1)^{3}=-1

(-1)^{4}=+1

...

(-1)^{(odd number)}=-1

(-1)^{(even number)}=+1 - This means (-1)
^{56}=+1 since 56 is an even number, (-1)^{57}=-1 since 57 is an odd number, and (-1)^{59}=-1. - This simplifies the numerator to:

5(-1) - 3(-1) + 4(1)

-5 + 3 + 4 = 2 - Plugging in -1 for x in the denominator yields:

2(-1 )+ 1

-2 + 1 = -1 - Combining the top and bottom of the fraction yields an answer of f(-1)=2/-1 = -2. The correct answer is A.

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