CAT Quantitative Aptitude Questions | CAT Algebra - Functions questions

The question is about Domain of Function. Our task is to find the domain of a function which contains log and square root. Functions is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept of Functions questions in the CAT Exam. Make sure you practice a lot of questions in CAT Functions Algebra to push your CAT preparation in the right direction. Functions as an idea is a fabulous idea if one can wrap their head around it the right way, and it has been one of the staple ideas tested by the CAT exam historically.

Question 14: Find the domain of: \\frac{1}{(1-log (9-x))}\\) + √(x+1)?

1. (-∞,9)
2. [-1,9)
3. [-1,9) excluding 0
4. (-1,9)

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Functions: Domain of a log function.

In the expression,
9-x > 0
=> x < 9

Also, 1-log ( 9-x) ≠ 0
=> log (9 – x) ≠ 1
=> 9-x ≠ 10
=> x ≠ -1
And, x + 1 > 0
=> x > -1

The question is "Find the domain of: \\frac{1}{(1-log (9-x))}\\) + √(x+1)?"

Hence the answer is "(-1,9)"

Choice D is the correct answer.