Let f (x) be an even function of the domain of definition on R, and if x > 0, f (x) = x (X-2), then find if X

f(x)=f(-x)=(-x)[(-x)-2]=x(x+2)

Given the function f (x) = x + 9 / X. find the definition and range of F (x)

When x ≠ 0, f (x) = x + 9 / X ≥ √ (9 / x) * x * 2 = 6, so f (x) ≥ 6, and because f (x) is an odd function, when x ＜ 0, f (x) ≤ - 6, so the range is (negative infinity, - 6) ∪ (6, positive infinity)

Given the function f (x) = 2 + log3x, X ∈ [1,9], find the maximum value of y = [f (x)] &# 178; + F (X & # 178;) and the value of X when y gets the maximum value

∵f（x）=2+log3x,x∈[1,9],
∴y=[f（x）]2+f（x2）=（2+log3x）2+（2+log3x2）
=(log3x) 2 + 6log3x + 6, let t = log3x
According to the meaning of the title, we can get 1 ≤ x ≤ 91 ≤ x2 ≤ 9 &; that is, 1 ≤ x ≤ 3, then t ∈ [0,1]
On [0,1], y = T2 + 6T + 6 = (T + 3) 2-3 increases monotonically
When t = 1, that is, x = 3, the function has a maximum value, ymax = 13

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