Find the domain of the definition of the function y = lxla)0 ≤xb)— ∞< x < +∞c)x < +∞d)0 ≤x < +∞Correct answer is option 'B'. Can you explain this answer?

Question

Find the domain of the definition of the function y = lxla)0 &#8804;xb)&#8212; &#8734;&#60; x &#60; +&#8734;c)x &#60; +&#8734;d)0 &#8804;x &#60; +&#8734;Correct answer is option 'B'. Can you explain this answer?

Answer

Method to Solve :

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:
(−∞,∞)
Set-Builder Notation:
{x|x∈R}
The absolute value expression has a V shape. The range of a positive absolute value expression starts at its vertex and extends to infinity.
Interval Notation:
[0,∞)
Set-Builder Notation:
{y|y≥0}
Determine the domain and range.
Domain: (−∞,∞),{x|x∈R}
Range: [0,∞),{y|y≥0}

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