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Inverse Function

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

MathematicsLet \(f:A\to B\) be a function. Which property is necessary and sufficient for \(f^{-1}:B\to A\) to also be a function?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 MathematicsFor (f:\mathbb{R}\to\mathbb{R}), (f(x)=3x-5), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to(0,\infty)) is given by (f(x)=e^{2x+1}), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is (f(x)=x^2+1) and (g:[1,\infty)\to\mathbb{R}) is (g(x)=\sqrt{x-1}), which statement is correct?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:[3,\infty)\to[1,\infty)) is defined by (f(x)=x^2-6x+10), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:A\to B) is both one-one and onto, which statement about (f^{-1}) is correct?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f(x)=\frac{x+2}{x-2}), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=2x-5), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=2x^3-1), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=3x-2) and (g:\mathbb{R}\to\mathbb{R}) by (g(x)=\frac{x+2}{3}), what is the relation between (g) and (f)?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:\mathbb{R}\setminus{0}\to\mathbb{R}\setminus{0}) is given by (f(x)=\frac{1}{x}), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=2x-5), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:A\to B) and (g:B\to A) satisfy (g\circ f=I_A) and (f\circ g=I_B), what is correct about (g)?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsIf (f:R\to R), (f(x)=x^3-7), what is (f^{-1}(x))?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsIf (f:R\to R), (f(x)=x^2-6x), why does an inverse function not exist?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsIf (f(x)=\frac{5x+1}{2}), what is (f^{-1}(x))?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsIf (f:R\to R), (f(x)=x^3-4), what is (f^{-1}(4))?Class 12Relations and FunctionsIntroduction to RelationsMedium MathematicsIf (f:R\to R), (f(x)=4x+7), what is the value of (f^{-1}(23))?Class 12Relations and FunctionsIntroduction to RelationsMedium