Functions

we have
f (x) = 2x3−15x2+36x+1
f' (x) = 6x62−30x+36
= 6(x2−5x+6)
= 6 (x - 2) (x - 3)
f (x) is increasing in [0, 2] and decreasing in [2, 3].
f (x) is many-one
f (0) = 1; f (2) = 29; f (3) = 28.
Range is [1, 29].
Hence, f (x) is many-one-onto.