Solve the Given Problem by Using Substitution $f ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 4$

Multiple Choice

Solve the given problem by using substitution.
Find the minimum value of $f ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 4$ subject to $y = 2 x$ .

A) $f _ { \min } = - 5$
B) $f _ { \min } = - 4$
C) $f _ { \min } = - 3$
D) $f _ { \min } = - 2$
E) $f _ { \min } = - 6$