Question

{f(x)=(p^(2)-1) tan^(-1)x +4(q^(2)+2q-3){(1)/(2+x^(2))}+(p+q)sgn(x^(2)-x+2) is continuous on R and f(x(1))=f(x_(2))AA x_(1) x_(2)in R then largest value of |p+q| is:​

Answer 1

Step-by-step explanation:

Given: f(x)=

cot

−1

(x

2

−α)

sgn(αx

2

+αx+1)

andf(x)iscontinousforallxεR

To find: Number of integer in the range of α

Sol: αx

2

+αx+1→isaquadratic

Whose discriminant=x

2

−4α

Now, for f(x) to be a valid function

sgn(αx

2

+αx+1)≥0forallxεR

⟹αx

2

+αx+1≥0⟹Discriminant≤0

⟹α(α−4)≤0

⟹α∈[0,4]

∴α∈[0,4]

⟹5 integers are in the range of α

Hence, the correct answer is 5

Answer By

Answer 2

Answer:

mujhe nhi aataa

Step-by-step explanation:

sorry sorry sorry