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Functions

by moneyman » Tue May 06, 2008 5:15 am
Need basic approach towards problemslike this:

For which of the following functions is f(a+b)=f(a)+f(b) for all positive numbers a and b ?

f(x)=x^2

f(x)=x+1

f(x)=Sq.rt(x)

f(x)=2/x

f(x)=-3x

Ans E
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by VP_RedSoxFan » Tue May 06, 2008 7:40 am
The general way to solve these is to say that whatever f(x) is, you need to apply to everything in the parentheses. Then you have to see which answer choice will mean that f(a+b) = f(a) + f(b)

For example:

[A]: f(x) = x^2 means that you have to square the "x" or whatever is in the parentheses and then see if it matches on both sides of the f(a+b) = f(a) + f(b) equation; f(a+b) = (a+b)^2 = a^2 + 2ab + b^2 and that does not necessarily equal f(a) + f(b) = a^2 + b^2

: f(x) = x + 1: f(a+b) = a + b + 1 and f(a) + f(b) = a + 1 + b + 1 = a + b + 2 so, this isn't right either

[C]: f(x) = sqrt(x): f(a+b) = sqrt(a+b) and f(a) + f(b) = sqrt(a) + sqrt(b); incorrect

[D]: f(x) = 2/x: f(a+b) = 2/(a+b) and f(a) + f(b) = 2/a + 2/b; those aren't the same either

[E]: f(x) = -3x: f(a+b) = -3(a+b) = -3a - 3b and f(a) + f(b) = -3a + -3b; so both sides of the f(a+b) = f(a) + f(b) will be equal with that function f.

Ans = E

Hope this helps, good luck!
Ryan S.
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