The problem of power function in high school mathematics It is known that the power function f (x) = x ^ (1 / 2p ^ 2 + P + 3 / 2), (P ∈ n), is an increasing function on (0, + ∞), and is an even function on the domain of definition (1) Find the value of P and write the explanation of the corresponding function f (x) (2) For the function f (x) obtained in (1), let g (x) = - Q [f (x)] + (2q-1) f (x) + 1, and ask whether there is a real number Q (q)

The problem of power function in high school mathematics It is known that the power function f (x) = x ^ (1 / 2p ^ 2 + P + 3 / 2), (P ∈ n), is an increasing function on (0, + ∞), and is an even function on the domain of definition (1) Find the value of P and write the explanation of the corresponding function f (x) (2) For the function f (x) obtained in (1), let g (x) = - Q [f (x)] + (2q-1) f (x) + 1, and ask whether there is a real number Q (q)

1. It is an increasing function on (0, + ∞)
So (- 1 / 2) P ^ 2 + P + 3 / 2 > 0
p^2-2p-3