It is known that the range of the function f (x) = 1 / 2x ^ 2-x + 3 / 2 defined on [1, M] is also [1, M], then the value of the real number m is
f(x)=(1/2)(x-1)^2+1
When x = 1, X belongs to [1, M], the image is on the right side of the symmetry axis. The function increases monotonically on [1, M]. When x = m, the function reaches the maximum, then
(1/2)(m-1)^2+1=m
(1/2)(m-1)^2=m-1
(1/2)(m-1)=1
m-1=2 m=3
m=3
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