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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}-{2}\to\mathbb{R}) and (f(x)=\frac{x+1}{x-2}), what type of function is (f)?Class 12Relations and FunctionsOne-one functionMedium MathematicsIf (f:\mathbb{R}-{-1}\to\mathbb{R}) and (f(x)=\frac{x}{x+1}), what type of function is (f)?Class 12Relations and FunctionsOne-one functionEasy MathematicsIf (f:\mathbb{R}-{2}\to\mathbb{R}) and (f(x)=\frac{1}{x-2}), what type of function is (f)?Class 12Relations and FunctionsOne-one functionEasy MathematicsIf (f(x)=\frac{1}{x+1}), what is ((f\circ f)(x))?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f(x)=\frac{3x-1}{2x+5}), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}-{1}\to\mathbb{R}-{2}) and (f(x)=\frac{2x+3}{x-1}), which statement is correct?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}-{-3}\to\mathbb{R}) and (f(x)=\frac{x-2}{x+3}), which value is excluded from the range?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f(x)=\frac{2x+3}{x-1}), then for (x\ne1), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f(x)=\frac{x-1}{x+1}), then for (x\ne -1), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\setminus{1}\to\mathbb{R}\setminus{2}) is given by (f(x)=\frac{2x+3}{x-1}), what is the value of (f^{-1}(5))?Class 12Relations and FunctionsFunctionsExpert MathematicsIf \(f:\mathbb{R}\to\mathbb{R}\) is given by \(f(x)=\frac{x}{1+x^2}\), what is the range of (f)?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\setminus{1}\to\mathbb{R}) is given by (f(x)=\frac{x^2-1}{x-1}), what is the range of (f)?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\frac{x^2-1}{x-1}), on which domain does it behave like (x+1)?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\setminus{-3}\to\mathbb{R}\setminus{2}) is given by (f(x)=\frac{2x-1}{x+3}), which statement about (f) is correct?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is considered as (f(x)=\frac{2x-1}{x+3}), which value must be removed from the domain to make it a function?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\frac{x^2}{1+x^2}), what is the range of (f)?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\setminus{2}\to\mathbb{R}\setminus{3}) is given by (f(x)=\frac{3x+1}{x-2}), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsExpert MathematicsIf \(f:\mathbb{R}-\left{-\frac{1}{2}\right}\to\mathbb{R}\) is defined by \(f(x)=\frac{3x-4}{2x+1}\), which real value will not occur in the range of (f)?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:\mathbb{R}\setminus{1}\to\mathbb{R}\setminus{2}) is defined by (f(x)=\frac{2x+3}{x-1}), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f(x)=\frac{2x-3}{x+4}), why is (x=-4) excluded from the domain?Class 12Relations and FunctionsFunctionsHard