If the power functions f (x) and G (x) pass through the points (2, root 2), (- 2,4) respectively, ① find the analytic expressions of F (x) and G (x); ② find f (x)

If the power functions f (x) and G (x) pass through the points (2, root 2), (- 2,4) respectively, ① find the analytic expressions of F (x) and G (x); ② find f (x)

Let f (x) = x ^ M
Bring in point (2, √ 2) to get: √ 2 = 2 ^ m solution: M = 1 / 2, that is: F (x) = x ^ (1 / 2)__ (i.e. root x)
Let g (x) = x ^ n
Bring in point (- 2,4) to get: 4 = (- 2) ^ n solution: n = 2, that is: G (x) = x ^ 2
(2) From √ X0
It's x1