You are here:

- Home
- Science
- Mathematics
- Advanced Math
- David Essner Preliminary

Advertisement

Let the function f satisfy f(xy) = f(x)/y for all positive numbers x,y. If f(5) = 10 then what is the value of f(8). Thank you.

In order to figure this out, I treated y like an arbitrary scaling factor, α, which scales the argument x in direct proportion and the output f(x) in inverse proportion. This is reminiscent of a hyperbola.

I rearranged the expression so that

α = f(x)/f(αx) = "constant"

the word "constant" being in parentheses because the expression should hold for any α (which is really y, for now). The expression also holds for all x, in particular x = 1, so with α = 5 we have f(α) = f(5) = 10 and

f(1) = αf(α) =5f(5) = 5･10 = 50.

Taking f(x) to be a hyperbola, we have f(x) = c/x, where c is a constant given by f(1) = c = 50.

Thus, f(8) = 50/8 = 6.25.

- Add to this Answer
- Ask a Question

Rating(1-10) | Knowledgeability = 10 | Clarity of Response = 10 | Politeness = 10 |

Comment | 10/10, would recommend. |

Advanced Math

Answers by Expert:

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related **Publications**

J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane**Education/Credentials**

M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math**Past/Present Clients**

Also an Expert in Oceanography