Let f (x) = x ^ (3 / 2 + K · 1 / 2 k-square) [K ∈ Z] (1) If f (x) is an even function and an increasing function on (0, + ∞), the analytic expression of F (x) is obtained (2) If f (x) is a decreasing function on (0, + ∞), find the value range of K

Let f (x) = x ^ (3 / 2 + K · 1 / 2 k-square) [K ∈ Z] (1) If f (x) is an even function and an increasing function on (0, + ∞), the analytic expression of F (x) is obtained (2) If f (x) is a decreasing function on (0, + ∞), find the value range of K

f(x)=x^(3/2+k*(1/2)^k) (k∈Z)
Because f (x) is an even function and an increasing function on (0, + ∞)
So 3 / 2 + k * (1 / 2) ^ k is even
So k = 1
(2)
Because f (x) is a decreasing function on (0, + ∞)
So 3 / 2 + k * (1 / 2) ^ k

Elden Ring Premiere

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