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When n is an odd integer, f(n)=3^n and when n is an even integer, f(n)

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When n is an odd integer, f(n)=3^n and when n is an even integer, f(n)  [#permalink]

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New post 31 Aug 2018, 01:18
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[Math Revolution GMAT math practice question]

When \(n\) is an odd integer, \(f(n)=3^n\) and when \(n\) is an even integer, \(f(n)=4^{\frac{n}{2}}\). What is the value of \(f(2^5)\)=?

\(A. 2^5\)
\(B. 3^{11}\)
\(C. 3^{12}\)
\(D. 3^{13}\)
\(E. 2^{32}\)

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When n is an odd integer, f(n)=3^n and when n is an even integer, f(n)  [#permalink]

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New post 31 Aug 2018, 01:23
MathRevolution wrote:
[Math Revolution GMAT math practice question]

When \(n\) is an odd integer, \(f(n)=3^n\) and when \(n\) is an even integer, \(f(n)=4^{\frac{n}{2}}\). What is the value of \(f(2^5)\)=?

\(A. 2^5\)
\(B. 3^{11}\)
\(C. 3^{12}\)
\(D. 3^{13}\)
\(E. 2^{32}\)


\(2^5=32\), which is even.

So\(, f(2^5)=f(32)=4^{\frac{32}{2}}\)=\(4^{16}=(2^2)^{16}=2^{32}\)

Ans. (E)
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Re: When n is an odd integer, f(n)=3^n and when n is an even integer, f(n)  [#permalink]

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New post 31 Aug 2018, 01:29
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MathRevolution wrote:
[Math Revolution GMAT math practice question]

When \(n\) is an odd integer, \(f(n)=3^n\) and when \(n\) is an even integer, \(f(n)=4^{\frac{n}{2}}\). What is the value of \(f(2^5)\)=?

\(A. 2^5\)
\(B. 3^{11}\)
\(C. 3^{12}\)
\(D. 3^{13}\)
\(E. 2^{32}\)


\(f(2^5)\)=\(f(32)\)
Since 32 is even, \(f(n)=4^{\frac{32}{2}}\)=\(f(n)=4^{16}\)
=\(f(n)=2^{32}\)
Answer E.
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Re: When n is an odd integer, f(n)=3^n and when n is an even integer, f(n)  [#permalink]

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New post 02 Sep 2018, 18:56
=>

Since \(n = 2^5\) is an even integer, \(f(2^5) = 4^{2^\frac{5}{2}}\)=\(4^{2^4}\)=\((2^{2)^16}=2^{32}.\)

Therefore, the answer is E.
Answer: E
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Re: When n is an odd integer, f(n)=3^n and when n is an even integer, f(n)   [#permalink] 02 Sep 2018, 18:56
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