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Onto 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}\to\mathbb{R}), (f(x)=ax^2+1), which statement is true?Class 12Relations and FunctionsOnto functionExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}), (f(x)=ax+b), when will (f) be onto?Class 12Relations and FunctionsOnto functionExpert MathematicsIf (h\circ g:A\to C) is onto, which statement must definitely be true?Class 12Relations and FunctionsOnto functionExpert MathematicsIf (g:A\to B) and (h:B\to C) are both onto, which statement about (h\circ g:A\to C) is correct?Class 12Relations and FunctionsOnto functionExpert MathematicsIf (g:\mathbb{R}\to[0,\infty)), (g(x)=x^2) and (h:[0,\infty)\to[1,\infty)), (h(t)=t+1), what is (h\circ g:\mathbb{R}\to[1,\infty))?Class 12Relations and FunctionsOnto functionExpert MathematicsIf (f:\mathbb{R}\to(0,\infty)), (f(x)=e^{x^3-x}), then (f) is onto becauseClass 12Relations and FunctionsOnto functionExpert MathematicsWhy is (f:\mathbb{R}\to[-1,1]), (f(x)=\frac{2}{\pi}\tan^{-1}x), not onto?Class 12Relations and FunctionsOnto functionExpert MathematicsIf \(f:\mathbb{R}\to(-1,1)\), \(f(x)=\frac{2}{\pi}\tan^{-1}x\), is (f) onto or not?Class 12Relations and FunctionsOnto functionExpert MathematicsFor \(f:\left(-\frac{\pi}{2},\frac{\pi}{2}\right)\to\mathbb{R}\), \(f(x)=\tan x\), what preimage of \(y\in\mathbb{R}\) proves onto property?Class 12Relations and FunctionsOnto functionExpert MathematicsIf \(f:\left[0,\frac{\pi}{2}\right]\to[-1,1]\), \(f(x)=\sin x\), why is (f) not onto?Class 12Relations and FunctionsOnto functionExpert MathematicsFor (f:[0,\pi]\to[-1,1]), (f(x)=\cos x), choose the correct statement.Class 12Relations and FunctionsOnto functionExpert MathematicsWhy is (f:\mathbb{R}\to\mathbb{Z}), (f(x)=\lceil x\rceil), onto?Class 12Relations and FunctionsOnto functionExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}), (f(x)=\lfloor x\rfloor+x), which statement about onto property is correct?Class 12Relations and FunctionsOnto functionExpert MathematicsFor (f:(0,\infty)\to[2,\infty)), (f(x)=x+\frac{1}{x}), what is the correct statement?Class 12Relations and FunctionsOnto functionExpert MathematicsIf (f:(0,\infty)\to(0,\infty)), (f(x)=x+\frac{1}{x}), why is (f) not onto?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 MathematicsIf (f:[1,\infty)\to[0,\infty)), (f(x)=x^2-1), what is the correct reason for onto property?Class 12Relations and FunctionsOnto functionExpert MathematicsIf (f:\mathbb{R}\to[-1,\infty)), (f(x)=x^2+2x), is (f) onto or not?Class 12Relations and FunctionsOnto functionExpert MathematicsA student says about the function \(h:\mathbb{R}\to\mathbb{R}\), where \(h(x)=x^3-3x\): “Since \(h(1)=h(-2)=-2\), \(h\) is not onto.” What is the correct evaluation of this statement?Class 12Relations and FunctionsOnto functionExpert MathematicsIf (f:\mathbb{Z}\to{m\in\mathbb{Z}:m\text{ is odd}}), (f(n)=2n+1), what is (f)?Class 12Relations and FunctionsOnto functionExpert