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For which of the following functions is g(c-d) = g(c) - g(d)

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For which of the following functions is g(c-d) = g(c) - g(d)  [#permalink]

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New post 11 Feb 2013, 10:09
2
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A
B
C
D
E

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Question Stats:

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For which of the following functions is g(c-d) = g(c) - g(d) for all positive numbers c and d?

A g(x) = x^3
B g(x) = x+5
C g(x) = \(\sqrt{3x}\)
D g(x) = 5x
E g(x) 15/x


Sometimes I read a problem 5 times in a row... and I still cannot understand what the question is asking. This was one of those... :x
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Re: For which of the following functions is g(c-d) = g(c) - g(d)  [#permalink]

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New post 14 Jan 2015, 23:50
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Hi All,

In these types of "function" questions, you can TEST VALUES (especially really simple ones) to find the correct answer.

Let's TEST...
C = 2
D = 1

The question asks us to find the equation that gives us the same result when...

g(2-1) = g(1) is calculated

and when

g(2) - g(1) is calculated

Answer A: g(X) = X^3
g(1) = 1^3 = 1
g(2) - g(1) = 2^3 - 1^3 = 8 - 1 = 7
1 does NOT = 7

Answer B: g(X) = X+5
g(1) = 1+5 = 6
g(2) - g(1) = (2+5) - (1+5) = 7 - 6 = 1
6 does NOT = 1

Answer C: g(X) = \sqrt{3X}
g(1) = \sqrt{3}
g(2) - g(1) = \sqrt{6} - \sqrt{3} = \sqrt{3}(\sqrt{2} - 1)
\sqrt{3} does NOT = \sqrt{3}(\sqrt{2} - 1)

Answer D: g(X) = 5X
g(1) = 5(1) = 5
g(2) - g(1) = 5(2) - 5(1) = 10 - 5 = 5
5 DOES = 5

Answer E: g(X) = 15/X
g(1) = 15/1 = 15
g(2) - g(1) = 15/2 - 15/1 = -15/2
15 does NOT = -15/2

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Re: For which of the following functions is g(c-d) = g(c) - g(d)  [#permalink]

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New post 11 Feb 2013, 10:18
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exploringm wrote:
For which of the following functions is g(c-d) = g(c) - g(d) for all positive numbers c and d?
A g(x) = x^3
B g(x) = x+5
C g(x) = \(\sqrt{3x}\)
D g(x) = 5x
E g(x) 15/x

Sometimes I read a problem 5 times in a row... and I still cannot understand what the question is asking. This was one of those... :x


This problem arises because in such type of questions the original function is not given. Instead, we have to find a function which can satisfy the constraint mentioned in the question.
Constraint--> g(c-d) = g(c) - g(d)--->(1), where (c-d), c, d are the values of x.
I am directly putting the value in the answer. You can verify the incorrect option by yourself.

Function as per option D is --->g(x) = 5x
Put the value of x = (c-d), we get --->g(c-d) = 5 (c-d) = 5c - 5d----(LHS)
Put the value of x = c, we get --->g(c) = 5 (c) = 5c ----(RHS)
Put the value of x = d, we get --->g(d) = 5 (d) = 5d----(RHS)

Equate RHS & LHS we get--> 5c - 5d = 5c - 5d
Thus equal.

So the answer is D.

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Re: For which of the following functions is g(c-d) = g(c) - g(d)  [#permalink]

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New post 16 Feb 2013, 13:21
In such questions these are the steps I find useful!!

1) The first step is to check whether you could solve the expression stated in the question( in case the expression is too long) or substitute the expression into the solutions in some manner so as to solve it quickly. If so, this is the quickest way out and usually with a little bit of practice, you can start judging whether this step would work or not before you place your pen on the paper to solve the question.

2) The next method is to find whether the solutions can be substituted into the original expression in some way that is fast and quick. This usually takes some time and hence, mostly does not work. However, if the answer options involve numbers instead of expressions, this might work better.

This method is only for those questions in which the answer options and the questions both contain expressions.

3) You could try substitution of base values to confirm.

.
exploringm wrote:
For which of the following functions is g(c-d) = g(c) - g(d) for all positive numbers c and d?

A g(x) = x^3
B g(x) = x+5
C g(x) = \(\sqrt{3x}\)
D g(x) = 5x
E g(x) 15/x


Sometimes I read a problem 5 times in a row... and I still cannot understand what the question is asking. This was one of those... :x
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Re: For which of the following functions is g(c-d) = g(c) - g(d)  [#permalink]

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New post 30 Apr 2013, 22:54
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Why is option C Wrong
\sqrt{3(c-d)} = \sqrt{(3c)}-\sqrt{(3d)}
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Re: For which of the following functions is g(c-d) = g(c) - g(d)  [#permalink]

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New post 30 Apr 2013, 23:08
Rajkiranmareedu wrote:
Why is option C Wrong
\sqrt{3(c-d)} = \sqrt{(3c)}-\sqrt{(3d)}

Option C says g(x) = \(\sqrt{3x}\)

So, g(c-d) = \(\sqrt{c-d}\)
g(c) = \(\sqrt{c}\)
g(d) = \(\sqrt{d}\)

We cannot say that \(\sqrt{c-d}\) = \(\sqrt{c}\) - \(\sqrt{d}\) for all values of c and d
So we cannot say that g(c-d) = g(c) - g(d) for all values of c and d.

Thus, option c is wrong.
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Re: For which of the following functions is g(c-d) = g(c) - g(d)  [#permalink]

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New post 04 Jul 2013, 19:48
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exploringm wrote:
For which of the following functions is g(c-d) = g(c) - g(d) for all positive numbers c and d?

A g(x) = x^3
B g(x) = x+5
C g(x) = \(\sqrt{3x}\)
D g(x) = 5x
E g(x) 15/x


Sometimes I read a problem 5 times in a row... and I still cannot understand what the question is asking. This was one of those... :x



put c = 3 and d = 2 or directly substitute c and d

we get option D, :)
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For which of the following functions is g(c-d) = g(c) - g(d)  [#permalink]

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New post 21 Jan 2015, 20:59
A g(x) = x^3

Power of "x" is changed, so IGNORE

B g(x) = x+5

"x" is added by constant, so IGNORE

C g(x) = \sqrt{3x}

Power of "x" is changed, so IGNORE

D g(x) = 5x

"x" is multiplied by constant 5, so required result is true


E g(x) 15/x

\(\frac{15}{x} = 15 * x^{-1}\)

Again power of "x" is changed, so IGNORE

Answer = D
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Re: For which of the following functions is g(c-d) = g(c) - g(d)  [#permalink]

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New post 18 Aug 2017, 01:01
Plug in values as c=4 and d=2
which will bring down the funtion in problem statement to g(2)=g(4)-g(2).
Now substituting the values in the option available as per the above equation LHS=RHS is option D.
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Re: For which of the following functions is g(c-d) = g(c) - g(d)  [#permalink]

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New post 22 Aug 2017, 11:09
For which of the following functions is g(c-d) = g(c) - g(d) for all positive numbers c and d?

A g(x) = x^3
B g(x) = x+5
C g(x) = 3x−−√3x
D g(x) = 5x
E g(x) 15/x


well its jus asking if they are the same or not, for that just substitute the value and we can find out.
Option D is the corect answer.
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Re: For which of the following functions is g(c-d) = g(c) - g(d)  [#permalink]

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New post 14 Sep 2018, 17:49
exploringm wrote:
For which of the following functions is g(c-d) = g(c) - g(d) for all positive numbers c and d?

A g(x) = x^3
B g(x) = x+5
C g(x) = \(\sqrt{3x}\)
D g(x) = 5x
E g(x) 15/x


We can let c = 2 and d = 1, and thus we are solving for both sides being equal when:

g(1) = g(2) - g(1)

Starting with answer choice E, we have 15/x:

g(1) = 15/1 = 15

g(2) = 15/2 = 7.5

g(2) - F(1) = 7.5 - 15 = -7.5

Since 15 does not equal -7.5, E is not correct.

Moving to D, we have 5x:

g(1) = 5 x 1 = 5

g(2) = 5 x 2 = 10

g(2) - g(1) = 10 - 5 = 5

Since 5 does equal 10 - 5, D might be correct.

For answer choice C, we have √3x:

g(1) = √(3*1) = √3

g(2) = √(3*2) = √6

Since √3 does not equal √6 - √3 = √3(√2 - 1), C is not correct.

For answer choice B, we have x + 5:

g(1) = 1 + 5 = 6

g(2) = 2 + 5 = 7

Since 6 does not equal 7 - 6 = 1, B is not correct.

For answer choice A, we have x^3:

g(1) = 1

g(2) = 8

Since 1 does not equal 8 - 1 = 7, A is not correct.

Since the only answer choice that is definitely not incorrect is D, it must be the correct answer.

Answer: D
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Re: For which of the following functions is g(c-d) = g(c) - g(d)  [#permalink]

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Re: For which of the following functions is g(c-d) = g(c) - g(d)   [#permalink] 18 Nov 2019, 03:56
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