Problem Solving

if the function F is defined by F(x)=x^2+1/x^2 for all nonzero numbers X, then F(-1/X)=
A. -1/f(x)
B. 1/f(x)
C. 1-f(x)
D. -f(x)
E. f(x)

rommysingh wrote:if the function F is defined by F(x)=x^2+1/x^2 for all nonzero numbers X, then F(-1/X)=
A. -1/f(x)
B. 1/f(x)
C. 1-f(x)
D. -f(x)
E. f(x)

One way to solve is to pick a number. In this case pick the number 2

F(x)=x^2 + 1/x^2
F(2)=2^2 + 1/2^2 = 4 + 1/4 = 4.25

F(-1/x) = (-1/x)^2 + 1/(-1/x)^2
F(-1/2) = (-1/2)^2 + 1/(-1/2)^2 = 1/4 + 4 = 4.25

Thefore F(x) = F(-1/x)

ans = e

An even easier way is just use the function.

Since f(x) = x² + (1/x²) for ANY value of x, we can use (-1/x) as our value. Hence we just REPLACE x with -1/x, as shown:

f(x) = x² + (1/x²), so

f(-1/x) = (-1/x)² + 1/(-1/x)²

or

f(-1/x) = 1/x² + (1/(1/x²)), which is just (1/x²) + x², the same thing we had for f(x).

Thus f(x) = f(-1/x), since they output the same result.

Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

if the function F is defined by F(x)=x^2+1/x^2 for all nonzero numbers X, then F(-1/X)=
A. -1/f(x)
B. 1/f(x)
C. 1-f(x)
D. -f(x)
E. f(x)




Consider (-1/x)^2= 1/x^2 and (1/(-1/x)^2)=x^2. So F(-1/x )=1/x^2 + x^2 = F(x).
So the answer is (E).