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Math Expert V
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The function f is defined for all numbers x by f(x) = |x + 3| + |x + 2  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 82% (01:42) correct 18% (02:14) wrong based on 60 sessions

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FRESH GMAT CLUB TESTS QUESTION

The function f is defined for all numbers x by f(x) = |x + 3| + |x + 2|. For which value of x, does f(x) = f(x - 1) ?

A. -3
B. -2
C. -1
D. 1
E. 2

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Re: The function f is defined for all numbers x by f(x) = |x + 3| + |x + 2  [#permalink]

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

|x + 3| + |x + 2| = |(x-1) + 3| + |(x-1) + 2|

|x + 3| = |x + 1|

The above equation satisfies only if x = -2

Ans B

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Joined: 13 May 2019
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The function f is defined for all numbers x by f(x) = |x + 3| + |x + 2  [#permalink]

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Given

The function f(x) = |x + 3| + |x + 2| ...... Equation A

To Find

For which value of x, does f(x) = f(x - 1) ?

Let us replace "x" by "x-1" in the function f(x) to get the function f(x-1):

f(x-1) = | (x-1) + 3 | + | (x-1) + 2 |

f(x-1) = |x+2| + |x+1| ...... Equation B

To find the value of x:

Equation A = Equation B

|x + 3| + |x + 2| = |x+2| + |x+1|

|x+3| = |x+1| ...... Equation C

Now, let us start substituting the values from the options to check if it fits the Equation c

1) When x = -3

|-3+3| = |-3+1|

|0| = |-2|

0 = 2 (Absurd)

So x cannot be -3

2) When x = -2

|-2+3| = |-2+1|

|1| = |-1|

1 = 1 ( Makes sense )

Since LHS = RHS , x=-2 is a sloution of the Equation C.

We do not need to check for the rest of the options as we have already got our answer, x=-2

So the correct answer is B.
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Re: The function f is defined for all numbers x by f(x) = |x + 3| + |x + 2  [#permalink]

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Bunuel wrote:

FRESH GMAT CLUB TESTS QUESTION

The function f is defined for all numbers x by f(x) = |x + 3| + |x + 2|. For which value of x, does f(x) = f(x - 1) ?

A. -3
B. -2
C. -1
D. 1
E. 2

equate for values f(x) = |x + 3| + |x + 2|

f(x) = f(x - 1)

test with answer values we see at -2 we get f(-2)=f(-3)
IMO B
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Re: The function f is defined for all numbers x by f(x) = |x + 3| + |x + 2  [#permalink]

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Bunuel wrote:

FRESH GMAT CLUB TESTS QUESTION

The function f is defined for all numbers x by f(x) = |x + 3| + |x + 2|. For which value of x, does f(x) = f(x - 1) ?

A. -3
B. -2
C. -1
D. 1
E. 2

I started with 2 in a jiffy, putting values I realized that if we put x -ve then we can cancel out terms to get f(x) = f(x - 1)
Substituting x= -2 we get it.

It all boils down to how fat we can get to the answer. I'm sharing a snapshot of my notepad.
Attachment: IMG_20190522_100059.jpg [ 1.61 MiB | Viewed 364 times ]

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I never gave up what I wanted- Re: The function f is defined for all numbers x by f(x) = |x + 3| + |x + 2   [#permalink] 21 May 2019, 21:34
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