Basic Function Question: Finding f(1/t) Using Homework Equations

[greenneub]

Homework Statement

I'm not sure what I'm doing wrong here.

Homework Equations

f(t) = t/(t+1)² find f(1/t)

The Attempt at a Solution

f(1/t) = 1/(t/(t+1)²)

= ((t+1)²)/t

= (t² + 2t +1)/t


The answer in my book says it's t/(t+1)², the original function. Is this an error?

 

[tiny-tim]

Hi greenneub!

f(t) = t/(t+1)² find f(1/t)

The Attempt at a Solution

f(1/t) = 1/(t/(t+1)²)

No, that's 1/f(t) …

you want f(x) where x = 1/t …

in other words, replace t by 1/t everywhere it occurs in t/(t+1)²