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Find the maximum value of f(x) = 183+x, x belongs to R [#permalink]
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14 May 2013, 18:45
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Find the maximum value of f(x) = 183+x, x belongs to R A. 12 B. 18 C. 20 D. 15
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Last edited by Bunuel on 15 May 2013, 02:31, edited 2 times in total.
Edited the question and moved to PS forum.



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Re: Find the maximum value of f(x) = 183+x, x belongs to R [#permalink]
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Vamshiiitk wrote: Find the maximum value of f(x) = 183+x, x belongs to R a) 12 b)18 c)20 d)15 Answer: b) 18 Reason: We have to find the max. value of f(x). Max value of 183+x will be 18 because the modulus will make 3+x>=0. Lower the value of 3+x, higher the value of 183+x=f(x). The lowest value of a modulus expression is 0, which implies f(x)=180=18.



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Re: Find the maximum value of f(x) = 183+x, x belongs to R [#permalink]
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15 May 2013, 02:34
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Re: Find the maximum value of f(x) = 183+x, x belongs to R [#permalink]
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15 May 2013, 02:52
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Vamshiiitk wrote: Find the maximum value of f(x) = 183+x, x belongs to R
A. 12 B. 18 C. 20 D. 15 The maximum value of 18  a where a >= 0 is 18 .The maximum value occurs when a is minimum and 3+x is minimum at 0 .When x = 3. Answer B
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Re: Find the maximum value of f(x) = 183+x, x belongs to R [#permalink]
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30 May 2013, 14:21
With numerous problems involving absolute value, we flip the signs inside the absolute value function if we know it to be a negative #. For example, 3x...if we know that X>3 then we: (3x) = 3+x. I'm guessing we don't do that here because in f(x) x cannot be less than 0? psychout wrote: Vamshiiitk wrote: Find the maximum value of f(x) = 183+x, x belongs to R a) 12 b)18 c)20 d)15 Answer: b) 18 Reason: We have to find the max. value of f(x). Max value of 183+x will be 18 because the modulus will make 3+x>=0. Lower the value of 3+x, higher the value of 183+x=f(x). The lowest value of a modulus expression is 0, which implies f(x)=180=18.



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Re: Find the maximum value of f(x) = 183+x, x belongs to R [#permalink]
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30 May 2013, 15:17
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WholeLottaLove wrote: With numerous problems involving absolute value, we flip the signs inside the absolute value function if we know it to be a negative #. For example, 3x...if we know that X>3 then we: (3x) = 3+x. I'm guessing we don't do that here because in f(x) x cannot be less than 0?
x can be negative, negative numbers belong to R. We can read the question as: Find the maximum value of \(f(x) = 183+x\), x belongs to R Find the maximum value of \(f(x) = 18(num\geq{0})\) Remeber that an abs value is a number positive or equal to zero ( never negative). So what in which case the operation \(18(num\geq{0})\) has the maxvalue? when the \(num\geq{0}\) is 0. Clearly \(180>181\) for example, so the max value is \(18\). For the sake of clarity: This case corespond to x=3, 33=0. For any other value of x the quantity 3x will result in a positive value that you will subtract to 18, obtaining a lesser value (of course).
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Re: Find the maximum value of f(x) = 183+x, x belongs to R [#permalink]
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30 May 2013, 18:17
Find the maximum value of f(x) = 183+x, x belongs to R
A. 12 B. 18 C. 20 D. 15
f(x) will be max when 3+x is minimum , and x= 3 is when it is minimum
Therefore the max value of f(x) = 18



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Re: Find the maximum value of f(x) = 183+x, x belongs to R [#permalink]
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31 May 2013, 02:18
WholeLottaLove wrote: With numerous problems involving absolute value, we flip the signs inside the absolute value function if we know it to be a negative #. For example, 3x...if we know that X>3 then we: (3x) = 3+x. I'm guessing we don't do that here because in f(x) x cannot be less than 0? psychout wrote: Vamshiiitk wrote: Find the maximum value of f(x) = 183+x, x belongs to R a) 12 b)18 c)20 d)15 Answer: b) 18 Reason: We have to find the max. value of f(x). Max value of 183+x will be 18 because the modulus will make 3+x>=0. Lower the value of 3+x, higher the value of 183+x=f(x). The lowest value of a modulus expression is 0, which implies f(x)=180=18. Actually f(x) can be less than 0. For example, if x=20, then f(20)=183+20=5 or if x=25, then f(25)=18325=4. Now, the question asks about the maximum value of f(x)=183+x (f(x) is equal to 18 minus some nonnegative value). To maximize f(x) we need to minimize 3+x. The minimum value of 3+x is 0, thus the maximum value of f(x)=183+x=180=0. Hope it helps. P.S. Notice that f(x) reaches its minimum for x=3 > f(3)=1833=180=0.
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Re: Find the maximum value of f(x) = 183+x, x belongs to R [#permalink]
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05 Feb 2014, 20:50
ButwhY wrote: Find the maximum value of f(x) = 183+x, x belongs to R
A. 12 B. 18 C. 20 D. 15 What does belong to R mean? Thank you.



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Re: Find the maximum value of f(x) = 183+x, x belongs to R [#permalink]
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05 Feb 2014, 23:40



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Re: Find the maximum value of f(x) = 183+x, x belongs to R [#permalink]
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Mixture problems tag is not required in this ButwhY wrote: Find the maximum value of f(x) = 183+x, x belongs to R
A. 12 B. 18 C. 20 D. 15
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