Let f: [2, ∞) → R be a f

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

Let f: [2, ∞) → R be a function defined by f(x) = x² - 4x + 5. The range of f is :

Options:

[1, ∞)

[4, ∞)

[5, ∞)

Correct Answer:

[1, ∞)

Explanation:

Given that, f(x) = x² - 4x + 5

Let (f(x)) = y

$y = x^2-4x+5⇒y=x^2-4x+4+1$

$y=(x-2)^2+1$

$y-1=(x-2)^2⇒(x-2)^2=y-1$

$x-2=\sqrt{y-1}⇒x=2+\sqrt{y-1}$

Now, if f is real valued function then.

$⇒ y-1≥0$

$⇒ y≥1$

The range of f is [1, ∞).