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Find the maximum value of f(x) = 18-|3+x|, x belongs to R

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Find the maximum value of f(x) = 18-|3+x|, x belongs to R [#permalink] New post 14 May 2013, 17:45
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Find the maximum value of f(x) = 18-|3+x|, x belongs to R

A. 12
B. 18
C. 20
D. 15
[Reveal] Spoiler: OA

Last edited by Bunuel on 15 May 2013, 01:31, 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) = 18-|3+x|, x belongs to R [#permalink] New post 14 May 2013, 19:47
Vamshiiitk wrote:
Find the maximum value of f(x) = 18-|3+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 18-|3+x| will be 18 because the modulus will make |3+x|>=0. Lower the value of |3+x|, higher the value of 18-|3+x|=f(x). The lowest value of a modulus expression is 0, which implies f(x)=18-0=18.
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Re: Find the maximum value of f(x) = 18-|3+x|, x belongs to R [#permalink] New post 15 May 2013, 01:34
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Vamshiiitk wrote:
Find the maximum value of f(x) = 18-|3+x|, x belongs to R

A. 12
B. 18
C. 20
D. 15


The absolute value is always more than or equal to zero, thus the least value of |3+x| is 0, therefore the max value of f(x) = 18-|3+x| is 18-0=18.

Answer: B.

Hope it's clear.

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Re: Find the maximum value of f(x) = 18-|3+x|, x belongs to R [#permalink] New post 15 May 2013, 01:52
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Vamshiiitk wrote:
Find the maximum value of f(x) = 18-|3+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) = 18-|3+x|, x belongs to R [#permalink] New post 30 May 2013, 13:21
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, |3-x|...if we know that X>3 then we: -(3-x) = -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) = 18-|3+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 18-|3+x| will be 18 because the modulus will make |3+x|>=0. Lower the value of |3+x|, higher the value of 18-|3+x|=f(x). The lowest value of a modulus expression is 0, which implies f(x)=18-0=18.
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Re: Find the maximum value of f(x) = 18-|3+x|, x belongs to R [#permalink] New post 30 May 2013, 14:17
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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, |3-x|...if we know that X>3 then we: -(3-x) = -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) = 18-|3+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 max-value? when the num\geq{0} is 0.
Clearly 18-0>18-1 for example, so the max value is 18.

For the sake of clarity:
This case corespond to x=-3, |3-3|=0. For any other value of x the quantity |3-x| 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) = 18-|3+x|, x belongs to R [#permalink] New post 30 May 2013, 17:17
Find the maximum value of f(x) = 18-|3+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) = 18-|3+x|, x belongs to R [#permalink] New post 31 May 2013, 01:18
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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, |3-x|...if we know that X>3 then we: -(3-x) = -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) = 18-|3+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 18-|3+x| will be 18 because the modulus will make |3+x|>=0. Lower the value of |3+x|, higher the value of 18-|3+x|=f(x). The lowest value of a modulus expression is 0, which implies f(x)=18-0=18.


Actually f(x) can be less than 0. For example, if x=20, then f(20)=18-|3+20|=-5 or if x=-25, then f(-25)=18-|3-25|=-4.

Now, the question asks about the maximum value of f(x)=18-|3+x| (f(x) is equal to 18 minus some non-negative 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)=18-|3+x|=18-0=0.

Hope it helps.

P.S. Notice that f(x) reaches its minimum for x=-3 --> f(-3)=18-|3-3|=18-0=0.
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Re: Find the maximum value of f(x) = 18-|3+x|, x belongs to R [#permalink] New post 05 Feb 2014, 19:50
ButwhY wrote:
Find the maximum value of f(x) = 18-|3+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) = 18-|3+x|, x belongs to R [#permalink] New post 05 Feb 2014, 22:40
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Re: Find the maximum value of f(x) = 18-|3+x|, x belongs to R   [#permalink] 05 Feb 2014, 22:40
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