CUET Preparation Today
The range of function f(x) = x2 - 2x + 2; x ∈ R is: |
[1, ∞) (0, ∞) (-∞, ∞) [-1, ∞) |
[1, ∞) |
Given $f(x)=x^2-2x+2$ Complete the square $f(x)=x^2-2x+1+1$ $f(x)=(x-1)^2+1$ Since $(x-1)^2 \ge 0$ for all $x \in \mathbb{R}$ Minimum value occurs when $(x-1)^2=0$ $x=1$ $f(1)=1$ Thus $f(x)\ge1$ The range is $[1,\infty)$. |
