Given that, f (x) = x2–4x+5Let f(x) = y⇒ y = x2–4x+5⇒ y = x2–4x+4+1⇒ y = (x-2)2+1⇒ y-1 = (x-2)2⇒ (x-2)2= y-1⇒ ⇒ Now, if f is real valued function then⇒ y-1 ≥ 0⇒ y ≥ 1∴ the range of f is [1, ∞).

Q. 444.5( 4 Votes )

Let f : [2, ∞) <s A. R

B. [1, ∞)

C. [4, ∞)

D. [5, ∞)

Class 12th Mathematics - Exemplar 1. Relations and Functions

Answer :

Given that, f (x) = x²–4x+5

Let f(x) = y

⇒ y = x²–4x+5

⇒ y = x²–4x+4+1

⇒ y = (x-2)²+1

⇒ y-1 = (x-2)²

⇒ (x-2)²= y-1

⇒

Now, if f is real valued function then

⇒ y-1 ≥ 0

⇒ y ≥ 1

∴ the range of f is [1, ∞).

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Let f : [2, ∞) <s A. RB. [1, ∞)C. [4, ∞)D. [5, ∞)

Let f : [2, ∞) <s A. R

B. [1, ∞)

C. [4, ∞)

D. [5, ∞)