Let f (x) be an even function on R, and f (x + 3) = - 1 / F (x), and if - 3 ≤ x ≤ - 2, f (x) = 4x, then the value of F (2014)

Let f (x) be an even function on R, and f (x + 3) = - 1 / F (x), and if - 3 ≤ x ≤ - 2, f (x) = 4x, then the value of F (2014)

Because f (x + 3) = - 1 / F (x)
&So f (x + 6) = - 1 / F (x + 3) & nbsp; substitute f (x + 3) = - 1 / F (x) into
&Then f (x) = f (x + 6) & nbsp;
&So the cycle is 6 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; so f (2014) = f (4)
&Since the function is even, f (4) = f (- 4)
&Substituting - 4 into f (x) = f (x + 6) & nbsp; yields f (- 4) = f (2)
&Because of even function
&So f (2) = f (- 2)
&When substituting - 3 ≤ x ≤ - 2, f (x) = 4x, f (- 2) = - 8
&Nbsp; so f (2014) = - 8
 
 
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The minimum value of function y = 2x-x + 1 divided by X-1 (x > 1)

Let m = X-1, then x = m + 1, the original formula = [(M + 1) ^ 2-m-1 + 1] / M = (m ^ 2 + m + 1) / M = m + 1 + 1 / M > = 1 + 2 = 3
When m = 1, that is, x = 2, the minimum value of 3 is obtained