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...

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.

Emma

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