Function f (x), X belongs to R, if for any real number x1, X2 has f (x1 + x2) + F (x1-x2) = 2F (x1) f (x2), prove that f (x) is even function

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• 1. Let y = f (x) (x belongs to R) satisfy f (x1) + F (x2) = f (x1 * x2) for any real number x1, X2, and prove that (1) f (1) = f (- 1) = 0 (2) f (x) is even function
• 2. Given that the function f (x) has: F (x1x2) = f (x1) + F (x2) for any x1, X2 on R, it is proved that f (x) is an even function
• 3. For the function f (x), f (x) is not zero, and X1 and X2 belong to any real number on R, there is f (x1 + x2) = 2 * f (x1) * f (x2). It is proved that f (x) is an even function
• 4. Trigonometric function symmetry If f (x) = sin (π / 4 x + π / 6), G (x) is symmetric with respect to x = 1, then G (x) is obtained There is also an analytic expression of y = 3sin (π / 2x + π / 6) with respect to x = 2 π symmetry
• 5. Trigonometric function symmetry If the image of y = sin (x + a) + radical three cos (x-a) is symmetric about the Y axis, then the value of a is Why is it wrong to calculate with x = 0, y = plus or minus 2? The answer is a = k π - π / 6
• 6. How to judge whether the domain is symmetric about the origin? For example: for the function f (x) = 3tan (1 / 2 x - π / 3), when discussing the parity of F (x), why is the domain not symmetric about the origin?
• 7. F (x) = 2x & # 178; + 4, X ∈ [- 2,2]
• 8. Try to discuss the parity of the function f (x) = x & # 178; - 2x + 3x > 0 = 0, x = 0 - X & # 178; - 2x-3x f（x）=x²-2x+3 x>0 =0 x=0 =x²-2x-3 x
• 9. F (x) = x ^ 2 + 2x judge the parity of function
• 10. Judge the parity of (1) f (x) = 1 / 2x. (2) f (x) = - 2x + 5. (3) f (x) = X4 + x2-1. (4) f (x) = 2x3-x By the way, write down its domain
• 11. Let f (x) (x ∈ R) satisfy f (x1 * x2) = f (x1) + F (x2) for any real number x1, X2, and prove that f (x) is an even function
• 12. It is known that the function f (x) is an even function on the set of real numbers R, and is a decreasing function on (0, + ∞). If x 10, then there is A.f（-x1）>f(-x2) B.f(-x1)=f(-x2) c.f(-x1)
• 13. Given the function y = F & nbsp; (x) (x ∈ R, X ≠ 0), for any non-zero real number x1, X2, f (x1x2) = f (x1) + F (x2), try to judge the parity of F (x)
• 14. The function FX = log (1 / 2) (x + 1) / (x-1) is known to judge the parity. It is proved that FX is an increasing function at (1, + ∞)
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• 17. There is a batch of 400 books sold in the first day and 40% of the total sold in the second day. At this time, there are still 200 books left. How many books are there in this batch? (urgent!
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