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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