Let f(x,y) = x^n * y^m. If x is doubled and y is halved, the new value of f is:

A. 2^(n-m) * f
B. 2^(m-n) * f
C. 2(n-m)...

Question

Let f(x,y) = x^n * y^m. If x is doubled and y is halved, the new value of f is:

A. 2^(n-m) * f
B. 2^(m-n) * f
C. 2(n-m) * f
D. 2(m-n) * f

Accepted Answer

The new value of f is 2^(n-m) * f. When x is replaced by 2x and y is replaced by y/2, we compute f(2x, y/2) = (2x)^n * (y/2)^m = 2^n * x^n * 2^(-m) * y^m = 2^(n-m) * x^n * y^m = 2^(n-m) * f(x,y).

Let f(x,y) = x^n * y^m. If x is doubled and y is halved, the new value of f is: A. 2^(n-m) * f B. 2^(m-n) * f C. 2(n-m) * f D. 2(m-n) * f