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erikvm
If \(f(x) =(x + \sqrt{3})^4\), what is the range of the function f(x)?

(A)\(\sqrt{3} < f(x) < 4\)

(B) f(x) >= 0

(C) f(x) < 0

(D) \(f(x) \neq{0}\)

Can someone please provide an explaination to this one?

MIN (F(X)) is when X= - \(\sqrt{3}\) So MIN(F(X)) = 0
MAX(F(X)) --> no boundary
(B) f(x) >= 0 is the answer
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Bunuel
erikvm
If \(f(x) =(x + \sqrt{3})^4\), what is the range of the function f(x)?

(A)\(\sqrt{3} < f(x) < 4\)

(B) f(x) >= 0

(C) f(x) < 0

(D) \(f(x) \neq{0}\)

Can someone please provide an explaination to this one?

f(x) equals to the even (4th) power of some number, thus it cannot be less than 0.
If \(x = - \sqrt{3}\), then f(x) = 0.

So, f(x) >= 0.

Answer: B.


Bunuel: Got this correct, I've no problem with either question or solution. But does calculus, suggested by the word "range", appear in GMAT ?
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Let

y =\( (x + \sqrt{3} )^4\)

=> \(\sqrt[4]{y}\) - \(\sqrt{3} \) = x

Square root can not take negative values and hence values should be '0' or more than than '0'.

Hence, Range is f(x) ≥ 0.

Answer C
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Hello from the GMAT Club BumpBot!

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