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ISRO-DEC2017-9

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

  1. injective and surjective
  2. surjective but not injective
  3. injective but not surjective
  4. neither injective nor surjective
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2 Answers

2 votes
2 votes

Injective means for every x there is unique value of f(x)

So here for x= 0 we have f(x) = 1

                  x= 1   f(x)= 24

                  x= 2   f(x)= 29

                  x= 2   f(x)= 28

So,every x has unique value of f(x)

Thus,it should be injective

Now coming to surjective part..if every element of set B(HERE [1,29]) is image of set A(here [0,3]) tehn it will be surjective but it is not the case.

So, answer should be C

But, according to below link answer is B

Please check if my logic or understanding is wrong

https://books.google.co.in/books?id=_RAwDwAAQBAJ&pg=PA32&lpg=PA32&dq=the%20function%20f%3A[0%2C3]%20-%3E%20[1%2C29]%20defined&source=bl&ots=2g8axUMuzW&sig=EZzVx5E7L-uP6rXmRZaLUXc4Lig&hl=en&sa=X&ved=0ahUKEwjz48Puw5rYAhXJsI8KHYgED3YQ6AEISTAF#v=onepage&q&f=false

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–1 votes
–1 votes

one to one (injective)----->A function for which every element of the range of the function corresponds to exactly one element of the domain.

onto (surjective)------>The function is surjective (onto) if each element of the range is mapped to by at least one element of the domain.

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