If f(x) = 3x - √x and g(x) = x^2...

[bluescale]

Hello,

This question is from EIV, 4th Ed., Chap 5, P. 79:

If f(x) = 3x - √x and g(x) = x^2, what is f(g(4)?

The strategy guide only gives 1 answer for this question. Shouldn't there be two answers since √x can equal 4 or -4?

My work:
1. g(4) = 4^2 = 16
2. f(16) = 3(16) - √16 = 48 -4 OR 48 +4 = 44 or 52

Thanks!

[siddarth.khangarot]

Hi, Since we are talking about √x, it implies only a positive root, on the other hand, if it were x^2, then the it would mean +x or -x.

When talking about roots, always consider positive roots on the GMAT.

[Ben Ku]

Thanks siddarth.khangarot. That is exactly right.

In sqrt(x), x must be positive, since you cannot take the square root of a negative number. With x^2, x can either be positive or negative. We don't know because when you square it, we lose the sign.

Hope that helps.