A function f(n) is defined as 2^ n-12 when n is odd and 3n2 when n is even. What is the value of f(f(f(3)))?

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PS · Problem Solving

505-555

Functions

A function $f(n)$ is defined as $2^{\frac{n-1}{2}}$ when $n$ is odd and $\frac{3n}{2}$ when $n$ is even. What is the value of $f(f(f(3)))$ ?

Correct answer marked below

\sqrt{2}

2

Correct

3

4

9

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Comments

NainaaOct 1

Thanks, the odd/even rule is clear from the definition. I just applied it one step at a time and got there.

Sparsh5d ago

Same here. The nested f(f(f(3))) looks intimidating but it's just three simple substitutions.

VaivaSep 9

Wait, for n odd the exponent is (n-1)/2, right? The formatting threw me off for a second.

MapSep 19

Yes, that's the exponent. Once I read it that way the first step made sense.

MirayaSep 14

Is this really 505-555? The function itself is easy but keeping track of which rule applies each time tripped me up.

ShreyaSep 16

I thought the same, but after the first step it calms down. Just don't mix up odd and even mid-way.

VaishnaviJun 27

Quick strategy note: since the input to the outer f depends on the previous output, just work inside out and check parity before each application.

What this question tests

Your ability to evaluate and compose functions, including unusual defined operations.

Applying function operations in the wrong order or ignoring domain restrictions.