Let `f:RtoR:f(x)=x^(2)+3`. Find the pre-images of each of the followin – InterviewSolution

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1.	Let `f:RtoR:f(x)=x^(2)+3`. Find the pre-images of each of the following under f: (i) 19 (ii) 28 (iii) 2
Answer» Given: `f(x)=x^(2)+3`. (i) Let x be pre-image of 19. Then, `f(x)-19impliesx^(2)+3=19impliesx^(2)=16impliesx=pm4`. `:.` 4 and -4 are the pre-images of 19. (ii) Let x be the pre-image of 28. Then, `f(x)=28impliesx^(2)+3=28impliesx^(2)=25impliesx=pm5`. `:.` 5 and -5 are the pre-images of 28. (iii) Let x be the pre-images of 2. Then, `f(x)=2impliesx^(2)+3=2impliesx^(2)=-1`. But, no real value of x satisfies the equation, `x^(2)=-1`. `:.` 2 does not have any pre-image under f.

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