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Class 11MathematicsRelations and FunctionsAlgebra of real functionsExpert
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If (f(x)=\sqrt{16-x^2}) and (g(x)=\frac{1}{x-1}), what is the domain of ((fg)(x))?

Answer and explanation

Correct answer: ([-4,4]\setminus{1})

The square root needs (16-x^2\ge 0), meaning (-4\le x\le 4), and the denominator needs (x\ne 1). The domain is the intersection of these conditions.

Related tags

Relations-FunctionsAlgebra-Real-FunctionsDomainProductAlgebra Of Real FunctionsRelations And FunctionsMathematicsClass 11 Mcq
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10 more MCQs
  1. 1If (f(x)=x+2) and (g(x)=3x), what is ((f+g)(x))?
  2. 2If f(x)=5x-1 and g(x)=2x+4, what is the value of (f-g)(x)?
  3. 3If \(f(x)=x+1\) and \(g(x)=x-1\), what is the value of \((fg)(x)\)?
  4. 4If \(f(x)=2x+6\) and \(g(x)=2\), what is the value of \(\left(\frac{f}{g}\right)(x)\)?
  5. 5If \(f(x)=x^2\) and \(g(x)=4\), what is the value of \((f+g)(2)\)?
  6. 6If \(f(x)=3x\) and \(g(x)=x+5\), find the value of \((f-g)(1)\).
  7. 7If f(x)=x+2 and g(x)=x+3, what is the value of (fg)(1)? Here, (fg)(x) denotes the product of f(x) and g(x).
  8. 8If f(x) = x^2 - 4 and g(x) = x - 2, what is the value of (f/g)(3)?
  9. 9If f(x) = x² + 1 and g(x) = 2x, then what is (f + g)(x) equal to?
  10. 10If \(f(x)=4x+7\) and \(g(x)=x-3\), what is \((f-g)(x)\)?
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