VJesus12 wrote:If function f(x) satisfies f(x)=f(x^2) for all x, which of the following must be true?
A. f(4)=f(2)f(2)
B. f(16)−f(−2)=0
C. f(−2)+f(4)=0
D. f(3)=3f(3)
E. f(0)=0
Let the function be defined as follows:
f(x) = 2.
Implication:
For any INPUT value, the OUTPUT value will always be 2, with the result that f(x) = f(x²) = 2.
Since the output value will always be 2, the answer choices imply the following:
A. f(4)=f(2)f(2) --> 2 = 2*2.
B. f(16)-f(-2)=0 --> 2-2 = 0.
C. f(-2)+f(4)=0 --> 2+2 = 0.
D. f(3)=3f(3) --> 2 = 3*2.
E. f(0)=0 --> 2=0.
Only the option in green is true.
Since A, C, D and E do not have to be true, eliminate A, C, D and E.
The correct answer is
B.
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