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Rational Function

Class 12 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf (f:\mathbb{R}\setminus{-1}\to\mathbb{R}), where (f(x)=\frac{x}{x+1}), why is it not onto?Class 12Relations and FunctionsReflexive relationExpert MathematicsIs (f:\mathbb{R}\setminus{-1}\to\mathbb{R}\setminus{1}), where (f(x)=\frac{x}{x+1}), onto?Class 12Relations and FunctionsReflexive relationExpert MathematicsIf (f:\mathbb{R}\to[-1,1)), (f(x)=\frac{x^2-1}{x^2+1}), which statement about (f) is correct?Class 12Relations and FunctionsOnto functionExpert MathematicsWhy is (f:\mathbb{R}\setminus{1}\to\mathbb{R}), (f(x)=\frac{x+1}{x-1}), not onto?Class 12Relations and FunctionsOnto functionExpert MathematicsIf (f:\mathbb{R}\setminus{1}\to\mathbb{R}\setminus{1}), (f(x)=\frac{x+1}{x-1}), which statement is correct?Class 12Relations and FunctionsOnto functionExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}), (f(x)=\frac{x^3}{1+x^2}), is (f) onto or not?Class 12Relations and FunctionsOnto functionExpert MathematicsThe function (f:(0,\infty)\to\mathbb{R}), (f(x)=x-\frac{1}{x}), is onto becauseClass 12Relations and FunctionsOnto functionExpert MathematicsFor (f:\mathbb{R}\setminus{2}\to\mathbb{R}\setminus{3}), (f(x)=\frac{3x+1}{x-2}), choose the correct statement.Class 12Relations and FunctionsOnto functionExpert MathematicsIf (f:\mathbb{R}\to[0,1]) and (f(x)=\frac{x^2}{1+x^2}), why is (f) not onto?Class 12Relations and FunctionsOnto functionHard MathematicsIf (f:\mathbb{R}\setminus{1}\to\mathbb{R}\setminus{2}) and (f(x)=\frac{2x+1}{x-1}), is (f) onto or not?Class 12Relations and FunctionsOnto functionHard MathematicsIf (f:\mathbb{R}\setminus{-2}\to\mathbb{R}\setminus{3}) and (f(x)=\frac{3x+1}{x+2}), choose the correct statement.Class 12Relations and FunctionsOnto functionHard MathematicsIf (f:\mathbb{R}\to[-\frac{1}{2},\frac{1}{2}]), (f(x)=\frac{x}{1+x^2}), which statement is correct?Class 12Relations and FunctionsOnto functionHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}), (f(x)=\frac{x}{1+x^2}), why is it not onto?Class 12Relations and FunctionsOnto functionHard MathematicsFor (f:\mathbb{R}\setminus{1}\to\mathbb{R}\setminus{1}), (f(x)=\frac{x+1}{x-1}), choose the correct statement.Class 12Relations and FunctionsOnto functionHard MathematicsChoose the correct option about (f:\mathbb{R}\to [0,1]), (f(x)=\frac{x^2}{1+x^2}).Class 12Relations and FunctionsOnto functionMedium MathematicsIf (f:\mathbb{R}\setminus{1}\to\mathbb{R}\setminus{1}), (f(x)=\frac{x+1}{x-1}), choose the correct statement about (f).Class 12Relations and FunctionsOnto functionMedium MathematicsIf (f:\mathbb{R}\to\mathbb{R}), (f(x)=\frac{x}{1+|x|}), then (f) is not onto becauseClass 12Relations and FunctionsOnto functionMedium MathematicsIf (f:\mathbb{R}\to[-1,1)), (f(x)=\frac{x^2-1}{x^2+1}), what is the correct statement?Class 12Relations and FunctionsOnto functionMedium MathematicsIf (f:\mathbb{R}\to[-1,1]), (f(x)=\frac{x^2-1}{x^2+1}), why is (f) not onto?Class 12Relations and FunctionsOnto functionMedium MathematicsIf (f:\mathbb{R}\setminus{1}\to\mathbb{R}\setminus{2}), (f(x)=\frac{2x+3}{x-1}), what form of (x) shows that (f) is onto?Class 12Relations and FunctionsOnto functionMedium