For p2 and x∈R, if the number of natural numbers in the range of fx=(x^2+2x+p)/(x^2+2x+2) is 3, then the value of p is equal to

Question

For p>2 and x∈R, if the number of natural numbers in the range of fx=(x^2+2x+p)/(x^2+2x+2) is 3, then the value of p is equal to

MARKS Content Team · Accepted Answer

Correct answer: (C) 5. Here, fx=1+(p-2)/(x+1^2+1)∈1,p-1 If there are 3 natural numbers in the range ⇒p-1=4⇒p=5

For $p > 2$ and $x \in R$ , if the number of natural numbers in the range of $f (x) = \frac{x^{2} + 2 x + p}{x^{2} + 2 x + 2}$ is $3,$ then the value of $p$ is equal to