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Domain Restriction

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

MathematicsOn (A=\mathbb{R}-{1}), (a*b=a+b-ab). Why is it closed in (A)?Class 12Relations and FunctionsBinary operationsHard MathematicsChoose the correct option for (f:[1,\infty)\to[0,\infty)), (f(x)=x^2-1).Class 12Relations and FunctionsOnto functionHard MathematicsChoose the correct statement for (f:[0,\infty)\to\mathbb{R}), (f(x)=x^3+1).Class 12Relations and FunctionsOnto functionHard MathematicsIf (f:[0,\infty)\to[0,\infty)), (f(x)=x^2), what is the correct statement?Class 12Relations and FunctionsOnto functionHard MathematicsWhat is the correct conclusion for (f:[1,\infty)\to [0,\infty)), (f(x)=x^2-2x+1)?Class 12Relations and FunctionsOnto functionHard MathematicsIf (f:[0,\infty)\to[0,\infty)), (f(x)=x^2), which statement is correct?Class 12Relations and FunctionsOnto functionMedium MathematicsWhat is the correct statement for (f:[0,\infty)\to\mathbb{R}), (f(x)=x^6+1)?Class 12Relations and FunctionsOne-one functionExpert MathematicsWhat is correct about the one-one nature of (f:(0,\infty)\to\mathbb{R}), (f(x)=\ln(x^2))?Class 12Relations and FunctionsOne-one functionExpert MathematicsWhich option is correct about the one-one nature of (f:\mathbb{R}\setminus{2}\to\mathbb{R}), (f(x)=\frac{x^2-4}{x-2})?Class 12Relations and FunctionsOne-one functionExpert MathematicsOn which domain restriction will (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^2), become one-one?Class 12Relations and FunctionsOne-one functionExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^2-6x+10), on which interval will (f) be one-one?Class 12Relations and FunctionsOne-one functionExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}), (f(x)=|x-2|), on which domain will (f) be one-one?Class 12Relations and FunctionsOne-one functionExpert MathematicsThe function (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^2+4x+7), will be one-one on which set?Class 12Relations and FunctionsOne-one functionExpert MathematicsIf (f:(-\infty,2]\to\mathbb{R}) and (f(x)=x^2), what is the correct statement about (f)?Class 12Relations and FunctionsOne-one functionExpert MathematicsIf (f:[0,\infty)\to\mathbb{R}), (f(x)=x^4), what is the one-one status of (f)?Class 12Relations and FunctionsOne-one functionHard MathematicsChoose the correct statement for the function (f:[0,\infty)\to\mathbb{R}), (f(x)=x^2).Class 12Relations and FunctionsOne-one functionHard MathematicsWhich of the following functions from ([0,\infty)) to (\mathbb{R}) is one-one?Class 12Relations and FunctionsOne-one functionMedium MathematicsIf (f:\mathbb{R}^{+}\to\mathbb{R}^{+}), (f(x)=x^2), where (\mathbb{R}^{+}) is the set of positive real numbers, what type is (f)?Class 12Relations and FunctionsOne-one functionEasy MathematicsIf \(f:\left[0,\pi\right]\to[-1,1]\), \(f(x)=\cos x\), what is the type of (f)?Class 12Relations and FunctionsFunctionsExpert MathematicsWhat type is \(f:\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\to[-1,1]\), \(f(x)=\sin x\)?Class 12Relations and FunctionsFunctionsExpert