For p2 and x∈ R , if the number of natural numbers in the range of f(x)=(x2 + 2 x + p/x2 + 2 x + 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 f(x)=(x2 + 2 x + p/x2 + 2 x + 2) is 3, then the value of p is equal to (A) 3 (B) 4 (C) 5 (D) 6

Tardigrade Admin · Accepted Answer

Here, f(x)=1+(p - 2/(x + 1)2 + 1)∈ (1 , p - 1] If there are 3 natural numbers in the range ⇒ p-1=4⇒ p=5

Q. 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

3

4

5

6

Here, $f (x) = 1 + \frac{p - 2}{( x + 1 ) ^{2} + 1} \in (1, p - 1]$
If there are $3$ natural numbers in the range
$\Rightarrow p - 1 = 4 \Rightarrow p = 5$

Q. For p>2 and x∈R , if the number of natural numbers in the range of f(x)=x2+2x+2x2+2x+p​ is 3, then the value of p is equal to

3

4

5

6

Here, f(x)=1+(x+1)2+1p−2​∈(1,p−1] If there are 3 natural numbers in the range ⇒p−1=4⇒p=5

Q. 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

Here, $f (x) = 1 + \frac{p - 2}{( x + 1 ) ^{2} + 1} \in (1, p - 1]$
If there are $3$ natural numbers in the range
$\Rightarrow p - 1 = 4 \Rightarrow p = 5$