The functions f and g are defined by f(x) = |2x +1| and g(x) = 3 for a

Question

The functions f and g are defined by f(x) = |2x +1| and g(x) = 3 for all numbers x. What is the least value of c for which f(c) = g(c)?

A. -4
B. -2
C. 0
D. 2
E. 4

Chethan92 · Answer

f(c) = |2c+1|
g(c) = 3. 
When c is -2.

f(c) = |-4+1| = 3 = g(c)

B is the answer

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Archit3110 · Answer

only at -2 we would get f(-2)= 3 which would be equal to g(-2)=3 
IMO B

CrackverbalGMAT · Answer

The functions f and g are defined by f(x) = |2x +1| and g(x) = 3 for all numbers x. What is the least value of c for which f(c) = g(c)?

#Approach 1:
f(c)= g(c)= 3
|2c +1| = 3

Case 1: 2c+1 ≥ 0 or c ≥-1/2

2c+ 1 = 3
2c=2
c=1.

Case 2: 2c+1 <0 or c < -1/2

-(2c +1) = 3
2c+1 = -3
2c = -4
c =-2

So, when c =1 or -2 , f(c)=g(c)=3. Since we are asked to find the least value of c, the answer should be option B i.e -2

#2: You can also plugin the answer options to get the correct answer.

Thanks,
  Clifin J Francis,
GMAT SME

BrushMyQuant · Answer

Given that  f(x) = |2x + 1|  and  g(x) = 3  and we need to find the least value of  c  for which f(c) = g(c)

To find f(c) we need to replace x with c in f(x) 
=> f(c) = |2c + 1|

g(c) will be 3 as g(x) does not depend on x

f(c) = g(c)
=> |2c + 1| = 3
=> 2c + 1 = 3, or 2c+1 = -3  Watch this video to know how to work with Absolute Value/Modulus problems  ]
=> 2c = 2 or 2c =-4
=> c = 1 or -2

Since we need to find the least value, so c = -2

So,  Answer will be B 
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

https://www.youtube.com/watch?v=b7JoMX0gk8M

bumpbot · Answer

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