If a function f: [2, ∞)arrow A defined by f(x) = x2 - 4x +5 is a bijection, then A is equal to

Question

If a function f: [2, ∞)arrow A defined by f(x) = x2 - 4x +5 is a bijection, then A is equal to (A)  R  (B)  [1,∞)  (C)  [2,∞)  (D) None of these

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<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/829d845346c98e7ac2917017a238cfa3-.jpeg" /> Given, function is f(x) = x2 -4 x + 5 which is defined as f: [2, ∞) arrow A Let y=x2-4x+5 ⇒ y=x2-4x+4+1 ⇒ y-1=(x-2)2 From the curve, we see that At x=2, f (2)=1, After that when we increase the value of x, the curve is increasing ∴ A=[1, ∞)

Q. If a function $f : [2, \infty) \to A$ defined by $f (x) = x^{2} - 4 x + 5$ is a bijection, then $A$ is equal to

$R$

$[1, \infty)$

$[2, \infty)$

None of these

Q. If a function f:[2,∞)→A defined by f(x)=x2−4x+5 is a bijection, then A is equal to

R

[1,∞)

[2,∞)

None of these

Given, function is f(x)=x2−4x+5 which is defined as f:[2,∞)→A Let y=x2−4x+5 ⇒y=x2−4x+4+1 ⇒y−1=(x−2)2 From the curve, we see that At x=2,f(2)=1, After that when we increase the value of x, the curve is increasing ∴A=[1,∞)

Q. If a function $f : [2, \infty) \to A$ defined by $f (x) = x^{2} - 4 x + 5$ is a bijection, then $A$ is equal to

$R$

$[1, \infty)$

$[2, \infty)$