GATE functions and relations

Question

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

Comments

No as they are asking for minimum in the worst case

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i mean they havent mentioned anything like this so how can we deduce this?

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In these kind of questions minimum rarely means anything else

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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?

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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 $$a(a + b)^*a + b(a + b)^*b$$