Let f:[0, ∞) arrow[0, ∞) be a function defined by f(x)=x2+(k2-3 k+2) x+k2-k. If f(x) is both injective and surjective, then the number of integers in the range of k is

Question

Let f:[0, ∞) arrow[0, ∞) be a function defined by f(x)=x2+(k2-3 k+2) x+k2-k. If f(x) is both injective and surjective, then the number of integers in the range of k is (A) 0 (B) 1 (C) 2 (D) 3

Tardigrade Admin · Accepted Answer

For f ( x ) to be injective and surjective f (0)=0 text and (- b /2 a )=0 ∴ k 2-3 k +2=0 text and k 2- k =0 ⇒ k =1 OR

0 f (0)=0 ⇒ k =0

Q. Let $f : [0, \infty) \to [0, \infty)$ be a function defined by $f (x) = x^{2} + (k^{2} - 3 k + 2) x + k^{2} - k$ . If $f (x)$ is both injective and surjective, then the number of integers in the range of $k$ is

0

1

2

3

For $f (x)$ to be injective and surjective
$f (0) = 0 and \frac{- b}{2 a} = 0$
$∴ k^{2} - 3 k + 2 = 0 and k^{2} - k = 0 \Rightarrow k = 1$
OR
$D > 0& f (0) = 0 \Rightarrow k = 0$

Q. Let f:[0,∞)→[0,∞) be a function defined by f(x)=x2+(k2−3k+2)x+k2−k. If f(x) is both injective and surjective, then the number of integers in the range of k is

0

1

2

3

For f(x) to be injective and surjective f(0)=0 and 2a−b​=0 ∴k2−3k+2=0 and k2−k=0⇒k=1 OR D>0&f(0)=0⇒k=0

Q. Let $f : [0, \infty) \to [0, \infty)$ be a function defined by $f (x) = x^{2} + (k^{2} - 3 k + 2) x + k^{2} - k$ . If $f (x)$ is both injective and surjective, then the number of integers in the range of $k$ is

For $f (x)$ to be injective and surjective
$f (0) = 0 and \frac{- b}{2 a} = 0$
$∴ k^{2} - 3 k + 2 = 0 and k^{2} - k = 0 \Rightarrow k = 1$
OR
$D > 0& f (0) = 0 \Rightarrow k = 0$