If f (x) = (M & # 178; - m-1) x ^ (M & # 178; + m + 3) is a power function, and if x ∈ (0, positive infinity), f (x) is an increasing function, find the analytic expression of F (x)?

If f (x) = (M & # 178; - m-1) x ^ (M & # 178; + m + 3) is a power function, and if x ∈ (0, positive infinity), f (x) is an increasing function, find the analytic expression of F (x)?

Because this function is a power function
So m ^ 2-m-1 = 1
M = 2 or M = - 1
If x belongs to (0, ∞), f (x) is an increasing function,
When m = 2, the original function is f (x) = x ^ 9. Obviously, X is an increasing function on (0, + ∞) and M = 2 holds
When m = - 1, the original function is f (x) = x ^ 3. Obviously, X is an increasing function on (0, + ∞), and M = - 1 holds
To sum up, the value of M satisfying the condition is - 1 or 2
F (x) = x ^ 9 or F (x) = x ^ 3