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

Question

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

Bunuel · Accepted Answer

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.

P.S. Please post PS questions in PS forum. Thank you.

Zarrolou · Answer

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).

psychout · Answer

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.

SrinathVangala · Answer

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

WholeLottaLove · Answer

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?

guptasulabh7 · Answer

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

Bunuel · Answer

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.

bytatia · Answer

What does belong to R mean?

Thank you.

Bunuel · Answer

R denotes the set of all  real numbers .

BrushMyQuant · Answer

Mixture problems tag is not required in this

pierjoejoe · Answer

i made this in desmos, hope it is useful https://www.desmos.com/calculator/al3gkabmwm

luisdicampo · Answer

Deconstructing the Question

We need the maximum value of

f(x)=18-|x+3|

for real   x  .

The key idea is that absolute value is always nonnegative:

|x+3|\ge 0

So  18-|x+3|  is largest when  |x+3|  is as small as possible.

Step-by-step

The smallest possible value of an absolute value is

0

So set

|x+3|=0

This happens when

x+3=0

x=-3

Now evaluate the function:

f(-3)=18-|-3+3|

=18-|0|

=18

Also, since

|x+3|\ge 0

we have

18-|x+3|\le 18

So  18  is the maximum value.

Answer B: 18

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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Perfect 805 Score Debrief by Julia

My Rewards