Question

Let f(x) = arccot(x ^ 2 + 4x + a ^ 2 - a) be a function defined R (0, pi 2 ] then the number of real values of alpha^ prime for which f(x) is ONTO is/are​

Answer 1

Answer:

Solution: f(x)=cot

−1

(x

2

−4x+α)

Range f(x)= Co -domain

cot

4

0⟶+∞

cot(

3

2π

)→−

3

1

x

2

−4x+α>−

3

1

−

2

(16−4α)

>−

3

1

16−4α<

3

2

⇒α>

4

1

(16−

3

2

)

∴ Hence, (B) is the correct option.