Given that a > 0 and a is not equal to 1, f (log a x) = [A / (a ^ 2 - 1)] / (x-1 / x) is 10 points Given that a > 0 and a is not equal to 1, f (log a x) = [A / (a ^ 2 - 1)] / (x-1 / x) 10 points Finding the expression of F (x) and judging the parity and monotonicity of F (x)

Given that a > 0 and a is not equal to 1, f (log a x) = [A / (a ^ 2 - 1)] / (x-1 / x) is 10 points Given that a > 0 and a is not equal to 1, f (log a x) = [A / (a ^ 2 - 1)] / (x-1 / x) 10 points Finding the expression of F (x) and judging the parity and monotonicity of F (x)

f(log a x)=[a/(a^2 -1)]/(x-1/x)
Let logax = t ∈ R, t ≠ 0, then x = a ^ t
f(t)=[a/(a^2-1)]/[a^t-a^(-t)]
∴f(x)=[a/(a^2-1)]/[a^x-a^(-x)] (x≠0)
f(-x)=[a/(a^2-1)]/[a^(-x)-a^x]=-f(x)
F (x) is an odd function
When a > 1,
When x ∈ (0, + ∞), a ^ x is an increasing function and - A ^ (- x) is an increasing function
The denominator a ^ x-a ^ (- x) is an increasing function and a positive value
1 / [a ^ x-a ^ (- x)] is a decreasing function
And a / (a ^ 2-1) > 0
Ψ f (x) is a decreasing function on (0, + ∞)
∵ f (x) is an odd function
∧ f (x) is also a decreasing function on (- ∞, 0)
When 0