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Class 11MathematicsRelations and FunctionsAlgebra of real functionsMedium
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If \\(f(x)=x+5\\) and \\(g(x)=2x-1\\), what is the value of the linear combination \\((2f-3g)(x)\\)?

Answer and explanation

Correct answer: \\(-4x+13\\)

The coefficients apply to the entire functions: \\((2f-3g)(x)=2f(x)-3g(x)=2(x+5)-3(2x-1)=2x+10-6x+3=-4x+13\\)。Hence, option A is correct. In option B, the sign of the \\(x\\)-term is handled incorrectly. In an exam, expand the brackets first and then combine like terms carefully.

Related tags

Relations-And-FunctionsAlgebra-Of-Real-FunctionsLinear-Combination-Of-FunctionsFunction-OperationsAlgebra 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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