If the image of F (x) and G (x) = (12) x is symmetric with respect to the line y = x, then the monotone increasing interval of F (4-x2) is______ ．

If the image of F (x) and G (x) = (12) x is symmetric with respect to the line y = x, then the monotone increasing interval of F (4-x2) is______ ．

The image of ∵ function f (x) and G (x) = (12) x is symmetric with respect to the line y = x, ∵ function f (x) is the inverse function of G (x) = (12) x, ∵ function f (x) = logx12, (x > 0), f (4-x2) = log (4 − x2) 12, and; 4-x2 ＞ 0, that is - 2 ＜ x ＜ 2, so the domain of definition of function f (4-x2) is (- 2,2). This problem is to find the decreasing interval of function T in the domain of definition. Because the decreasing interval of function T = 4-x2 in the domain of definition is [0,2], the monotone increasing interval of function f (4-x2) is [0,2], so the answer is: [0,2]