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Question

(i) Find the domain of the function f(x)=x2+2x+1x28x+12.

(ii) Let A={8,11,15,12,15,18,23} and f be function from AN, such that f(x) is the highest prime factor of x. Find f and its range.


Solution

(i) Here, f(x)=x2+2x+1x28x+12

Since, f(x) is a rational function of x.

Hence, f(x) assumes real value of x except for those values of x for which x28x+12=0.

  x28x+12=0  (x6)(x2)=0  x=2 and 6

  Domain of function = R{2,6}

(ii) Given, A={8,11,15,12,18,23} and f is a function from AN such that 

f(x) = Highest prime factor of x

 f(8) = Highest prime factor of 8 = 2

f(11) = Highest prime factor of 11 = 11

f(12) = Highest prime factor of 12 = 3

f(15) = Highest prime factor of 15 = 5

f(18) = Highest prime factor of 18 = 3

f(23) = Highest prime factor of 23 = 23

f={(8,2),(11,11),(12,3),(15,5),(18,3),(23,23)}

Hence, range of f is {2,11,3,5,23}


Mathematics

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