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Real Functions

Class 11 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf \(f(x)=\sqrt{x-1}\) and \(g(x)=x-5\), what is the domain of \(\left(\frac{f}{g}\right)(x)\)?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeExpert MathematicsLet \(f:\mathbb{R}\to\mathbb{R}\) be an even function and \(g:\mathbb{R}\to\mathbb{R}\) be an odd function. Which statement about \(h(x)=f(g(x))\) is always true?Class 11Relations and FunctionsAlgebra of real functionsExpert MathematicsIf \(f(x)=\sqrt{x-2}\) and \(g(x)=\sqrt{10-2x}\), what is the domain of \((f+g)(x)\)?Class 11Relations and FunctionsAlgebra of real functionsExpert MathematicsIf f(x) = √(x + 2) and g(x) = 1/(x − 1), what is the domain of (fg)(x)?Class 11Relations and FunctionsAlgebra of real functionsMedium MathematicsIf \(f(x)=x^2\) and \(g(x)=2x+1\), what is the value of \((f+g)(-2)\)?Class 11Relations and FunctionsAlgebra of real functionsExpert MathematicsLet \(f(x)=\frac{1}{x}\) and \(g(x)=x^2\). Find the domain of \((f\circ g)(x)\).Class 11Relations and FunctionsAlgebra of real functionsExpert MathematicsIf \(f(x)=x^2+ax\) and \(g(x)=bx+1\), and \((f-g)(x)=x^2-5x-1\), what is the value of \(a-b\)?Class 11Relations and FunctionsAlgebra of real functionsHard MathematicsSuppose the real functions \(f\) and \(g\) both have domain \(\mathbb{R}\). Which condition ensures that the quotient function \(\frac{f}{g}\) also has domain \(\mathbb{R}\)?Class 11Relations and FunctionsAlgebra of real functionsHard MathematicsIf f(x) = x² − 4 and g(x) = |x| − 2, for which values of x is (f − g) = 0?Class 11Relations and FunctionsAlgebra of real functionsHard MathematicsIf \(f(x)=x+1\), \(g(x)=x-1\), and \((af+bg)(x)=5x+1\), what is the value of \(a+b\)?Class 11Relations and FunctionsAlgebra of real functionsHard MathematicsIf \(f(x)=x^2+ax\) and \(g(x)=2x-a\), and \((f+g)(1)=7\), what is the value of \(a\)?Class 11Relations and FunctionsAlgebra of real functionsHard MathematicsIf f(x) = 2x + 1 and g(x) = 3x − 4, what is (fg)(−1)?Class 11Relations and FunctionsAlgebra of real functionsEasy MathematicsIf \(f(x)=\frac{1}{\sqrt{x-1}}\) and \(g(x)=x^2\), what is the domain of \((f+g)(x)\)?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeMedium MathematicsIf \(f(x)=2x+5\) and \(g(x)=5-2x\), what is the value of \((f+g)(x)\)?Class 11Relations and FunctionsAlgebra of real functionsMedium MathematicsIf \(f(x)=2x-1\) and \(g(x)=x^2\), what is the value of \((f+g)(-2)\)?Class 11Relations and FunctionsAlgebra of real functionsMedium MathematicsIf \(f(x)=3x^2\) and \(g(x)=2x+1\), what is the value of \((f+2g)(x)\)?Class 11Relations and FunctionsAlgebra of real functionsMedium MathematicsIf \(f(x)=x+4\) and \(g(x)=4-x\), what is the product function \((fg)(x)=f(x)g(x)\) equal to?Class 11Relations and FunctionsAlgebra of real functionsMedium MathematicsIf \(f(x)=2x+1\) and \(g(x)=x-2\), what is the value of \((3f+2g)(x)\)?Class 11Relations and FunctionsAlgebra of real functionsMedium MathematicsIf \(f(x)=x^2-1\) and \(g(x)=x^2+1\), what is the range of \((g-f)(x)\)?Class 11Relations and FunctionsAlgebra of real functionsMedium MathematicsLet \(f:A\to B\) and \(g:B\to C\). Which composite function is obtained by applying \(f\) first and then \(g\) to each element of \(A\)?Class 11Relations and FunctionsAlgebra of real functionsMedium