Domain of the function f given by f(x) = 2 – |x – 5| is

Question

It is taken from the chapter "relations and functions" from class 11th. This questions also have options i.e., 

a) R^+

b) R - {5}

c) R - {-5}

d) R 

Answer 1

Remember the idea behind domain: it's the set of all numbers you could plug in and get an answer out of the other end. In other words, if you mentioned it to your calculator, would it respond "MATH ERROR"? If not, it's in the domain!

Let's look at your specific problem: You start by subtracting from X. Is there any number that can't do this? Nope! So far, the domain remains all real numbers.

After you subtract, you are taking the absolute value. Again, it has no holes, so keep that domain.

Finally, you are subtracting the result from 2. Once again, there is no gap there, either. Your final answer is yet again all real numbers. We don't have the exact symbol in the text editor, so imagine my "R" has a heavy spine.