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

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The functions f and g are defined by f (x) = |2x +1| and g( [#permalink] New post 11 Dec 2017, 10:34
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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)?

enter your value

[Reveal] Spoiler: OA
\(-2\)

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Re: The functions f and g are defined by f (x) = |2x +1| and g( [#permalink] New post 12 Dec 2017, 04:52
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Carcass wrote:
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)?

enter your value

[Reveal] Spoiler: OA
OA in 24h


Here,

we need to find the least value of c

therefore

|2x +1| = 3

or 2x +1 = 3

or x = 1

therefore when c= 1 we have f (c) = g (c)

However we can also write as

|2x +1| = 3

or 2x + 1 = -3

or x = -2

therefore when c= -2 we have f (c) = g (c).

Hence the least value is = -2
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Re: The functions f and g are defined by f (x) = |2x +1| and g( [#permalink] New post 17 Feb 2019, 09:19
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Carcass wrote:
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)?

enter your value

[Reveal] Spoiler: OA
\(-2\)


If f(x) = |2x + 1|, then f(c) = |2c + 1|
If g(x) = 3, then g(c) = 3

So, the equation f(c) = g(c) becomes |2c + 1| = 3

So, EITHER 2c + 1 = 3 OR 2c + 1 = -3

Let's solve each equation

Take: 2c + 1 = 3
Subtract 1 from both sides to get: 2c = 2
Solve: c = 1

Take: 2c + 1 = -3
Subtract 1 from both sides to get: 2c = -4
Solve: c = -2

What is the LEAST value of c for which f(c) = g(c)?
The solutions are c = 1 and c = -2

The LEAST value is -2

Answer: -2

Cheers,
Brent
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Re: The functions f and g are defined by f (x) = |2x +1| and g(   [#permalink] 17 Feb 2019, 09:19
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