SOLUTION: if f(x)=2x^2-(1/x)-2, then the value of f(1/x)is a. 1/2x^2-1/x-2 b. 2x^2-1/x-2 c. 2/x^2-x-2 d. 1/2x^2-x-2

Algebra ->  Inequalities -> SOLUTION: if f(x)=2x^2-(1/x)-2, then the value of f(1/x)is a. 1/2x^2-1/x-2 b. 2x^2-1/x-2 c. 2/x^2-x-2 d. 1/2x^2-x-2      Log On


   

Question 972749: if f(x)=2x^2-(1/x)-2, then the value of f(1/x)is
a. 1/2x^2-1/x-2
b. 2x^2-1/x-2
c. 2/x^2-x-2
d. 1/2x^2-x-2
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you replace the argument of x with the argument of 1/x.

start with f(x) = 2x^2 - (1/x) - 2

replace x with 1/x and you get:

f(1/x) = 2 * (1/x)^2 - (1 / (1/x)) - 2

(1/x)^2 is the same as 1^2 / x^2 which is equal to 1/x^2
2 * (1/x)^2 becomes 2 * (1/x^2) which becomes 2/x^2

1/(1/x) = 1 * (x/1) = x

your equation of:

f(1/x) = 2 * (1/x)^2 - (1 / (1/x)) - 2 becomes:

f(1/x) = 2/x^2 - x - 2.

that looks like selection c.