How Does the Function f(1/x) Simplify to the Book's Answer?

[CarlosRamos]

I'm having difficulties in obtaining the book/calculator answer to the function
f(x) = (x-1)(x+5) when f(1/x).

The book answer is: [(1-a)(1+5a)]/a
The answer I get is: 1/(a^2) + 4a - 5
. or : (1 + 4a - 5a^2)/a^2
. or : [(1 + 4a)/a^2] - 5

I know that all these answers are possible answers, but I can't for the life of me figure out how the book got the answer (I've also checked with a graphing calculator, and received the same answers)

- Thanks :)

 

[courtrigrad]

f(x) = (x-1)(x+5)

Then f(\frac{1}{a}) = (\frac{1}{a}-1)(\frac{1}{a} +5 )

Try working with the fractions (i.e. adding and subtracting) within the parentheses, then multiply them and see what you get.

Also it shoud be \frac{(1-a)(1+5a)}{a^{2}}