Question

SECTION - B
17. Prove that f: N - N defined by S(x) = x2 + x + 1 is one-one but not onto.​

Answer 1

Hello Friend,

Given equation is

S(x) = x² + x +1

differentiating the given equation we get

S'(x)= 2x+1

S'(x) = 0

we get x= -1/2

as f'(x) > 0 , f(x) is Increasing function

if you plot the graph

you can see that function is increasing as every mapping has unique value. Every value is greater than last value and less than next value

So its one one function.

And you can see that on Y - axis between 3 and 7 there 4 ,5 , 6 values which are in co domain but not in range

Thus this gives that its not onto function.

Hence Proved!

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