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
The OA is the option B.
I think the correct option is E. Why is B? May any expert clarify this? Thanks in advanced.
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If function f(x) satisfies f(x)=f(x^2) . . . .
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Let the function be defined as follows: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
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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