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Functions

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}\to\mathbb{R}) is defined by (f(x)=x^2+2x), what is the range of (f)?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=x^2), why does (f^{-1}) not exist as an ordinary function?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=2x+3) and (g:\mathbb{R}\to\mathbb{R}) by (g(x)=\frac{x-3}{2}), which statement is correct?Class 12Relations and FunctionsFunctionsHard MathematicsIf \(f:\mathbb{R}\setminus{0}\to\mathbb{R}\setminus{0}\) is defined by \(f(x)=\frac{1}{x}\), what is (f\circ f)?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:A\to B) and (g:B\to A) satisfy (f\circ g=I_B), what conclusion about (f) is definitely true?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:A\to B) and (g:B\to A) satisfy (g\circ f=I_A), what conclusion about (f) is definitely true?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=x^3-3x), it is not one-one. Which example proves this correctly?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=ax^2) with (a\neq0), why is (f) not one-one?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=ax+b), when will (f) be one-one and onto?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f={(1,2),(1,3),(2,4)}), why is this not a function?Class 12Relations and FunctionsFunctionsHard MathematicsOn the set (A={1,2,3}), (f={(1,2),(2,3),(3,1)}) is given. Which statement about (f) is correct?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:A\to B) is a function, which situation violates the definition of a function?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:\mathbb{R}\to[3,\infty)) is defined by (f(x)=x^2-4x+7), which statement is correct for (f)?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f(x)=x^2-4x+7), what is its minimum value?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:(0,\infty)\to\mathbb{R}) is defined by (f(x)=\ln x), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:\mathbb{R}\to(0,\infty)) is defined by (f(x)=e^x), which statement about (f) is correct?Class 12Relations and FunctionsFunctionsHard MathematicsIf \(f:\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\to[-1,1]\) is defined by \(f(x)=\sin x\), what type of function is (f)?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=\sin x), why is (f) not onto?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=x^3+x), what is the correct reason for (f) being one-one?Class 12Relations and FunctionsFunctionsHard MathematicsIf (A) has (5) elements and (B) has (3) elements, how many one-one functions are possible from (A) to (B)?Class 12Relations and FunctionsFunctionsHard