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The function f: [0,3]$\rightarrow$[1,29] defined by f(x) = $2x^{3} - 15x^{2} + 36x +1$ where x is an integer is

(a) injective and surjective

(b) surjective but not injective

(C) injective but not surjective

(d) neither injective not surjective
in Mathematical Logic by (39 points) | 34 views
No as they are asking for minimum in the worst case
i mean they havent mentioned anything like this so how can we deduce this?
In these kind of questions minimum rarely means anything else
toc doubt, how to tell if a language is regular or not?

eg like 1.{wxw$^r$ | w,x ϵ {a,b}$^*$} this is regular as if we substitute w=w$^r$ with ϵ then only x will remain and generate all languages.

but 2. {wxw$^r$ | w,x ϵ {a,b}$^+$} here we can’t substitute ϵ so how this is regular?
But here we can choose w to be a or b only and in between everything will be x, so we have to match first and last character only.

R.E will be $$a(a + b)^*a + b(a + b)^*b$$

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