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Range of a rational function by the discriminant method

This type of question, asked 2 times: 31 Jan 2023, 7 Apr 2025. All 2 questions below, oldest first.

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  1. Question 1

    31 Jan 2023

    170
    Let f:R−{2,6}→R\mathbf{f:R - \{ 2,6\} \rightarrow R} be real valued function defined as f(x)=x2+2x+1x2−8x+12f(x) =\frac{x^{2}+ 2x + 1}{x^{2}- 8x + 12}. Then range of ff is

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  2. Question 2

    7 Apr 2025

    129
    If the range of the function f(x)=5−xx2−3x+2f\left( x \right)=\frac{5 -x}{x^{2}- 3x+ 2}, x≠1,2x\neq 1,2, is (−∞,α)∪[β,∞)\left( - \infty,\alpha \right)\cup\left\lbrack \beta,\infty \right), then α2+β2\alpha^{2}+\beta^{2} is equal to :

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