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Algebra Of 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)=x^2 and g(x)=x+1, then what is (f∘g)(x)-(g∘f)(x)?Class 11Relations and FunctionsAlgebra of real functionsHard MathematicsIf \(f(x)=\frac{1}{x-1}\) and \(g(x)=x+1\), what are the real solutions of \((fg)(x)=1\)?Class 11Relations and FunctionsAlgebra of real functionsHard MathematicsIf \(f(x)=\frac{1}{x^2+1}\) and \(g(x)=x^2+1\), what is the range of the product function \((fg)(x)\)?Class 11Relations and FunctionsAlgebra of real functionsHard MathematicsIf \(f(x)=\frac{x-1}{x+1}\) and \(g(x)=\frac{x+1}{x-1}\), what is the simplified form of \((f-g)(x)\)?Class 11Relations and FunctionsAlgebra of real functionsHard MathematicsIf \(f(x)=\frac{x^2-1}{x+1}\) and \(g(x)=x-1\), for which real values of \(x\) do \(f\) and \(g\) have the same value?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeHard MathematicsIf \(f(x)=x^2\) and \(g(x)=|x|\), for which real values of \(x\) is \((f-g)(x)=0\)?Class 11Relations and FunctionsAlgebra of real functionsHard 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 MathematicsIf f(x)=|x|+x and g(x)=|x|-x, what is their pointwise product (fg)(x)?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 \(f(x)=x^2+2x\) and \(g(x)=3x-5\), what is the expression for \((2f-3g)(x)\)?Class 11Relations and FunctionsAlgebra of real functionsHard MathematicsIf \(f(x)=x^2\), \(g(x)=2x\), and \(h(x)=1\), what is the simplified form of the combined function \((f-g+h)(x)\)?Class 11Relations and FunctionsAlgebra of real functionsHard MathematicsIf \(f(x)=x^2-5x+6\) and \(g(x)=x-2\), for which value of \(x\) is \(\left(\frac{f}{g}\right)(x)=0\)?Class 11Relations and FunctionsAlgebra of real functionsHard MathematicsIf f(x)=x²+4x+5 and g(x)=x²−4x+5, what is the value of the product function (fg)(0)?Class 11Relations and FunctionsAlgebra of real functionsHard MathematicsIf \(f(x)=x^2-2x\) and \(g(x)=3x-1\), what is the value of \((2f-3g)(x)\)?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 \(f(x)=x^2+3x\) and \((f-g)(x)=2x^2-x\), what is \(g(x)\)?Class 11Relations and FunctionsAlgebra of real functionsHard MathematicsIf \(f(x)=3x-2\) and \((f+g)(x)=x^2+x\), what is the expression for \(g(x)\)?Class 11Relations and FunctionsAlgebra of real functionsHard MathematicsIf \(f(x)=2x-5\) and \(g(x)=3-x\), what is the value of \((f+g)(4)\)?Class 11Relations and FunctionsAlgebra of real functionsHard MathematicsIf f(x)=x²+3x and g(x)=x²−3x, what is the nature of (f+g)(x)?Class 11Relations and FunctionsAlgebra of real functionsMedium MathematicsIf f(x)=|x−2| and g(x)=x−2, for which x is (f−g)(x)=0 true?Class 11Relations and FunctionsAlgebra of real functionsMedium