A Complicated Function

Algebra Level 3

$f$ is a function on the positive reals that satisfies $f( x^2 + 1) ^{\frac {1} {\sqrt{x}} } = x ^{ \frac {6}{x} }$ , what is the value of $f( 82)$ ?

The answer is 81.

1 solution

Arron Kau Staff
May 13, 2014

Substitute $x=9$ into the equation, $f(82) ^{ \frac {1} {3} } = 9^ {\frac {6}{9} } = 9^ {\frac{2}{3} }$ . Hence $f(82) = 9^ {\frac{2}{3} \times 3} = 9^2 = 81$ .

f(a)=b does not imply that f(a^3)=b^3. Why is it so in this case ?

Des O Carroll - 6 years, 1 month ago

A Complicated Function

The answer is 81.

1 solution

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