Question

Q1) Find the domain and range of f(x)=1/√x+|x|.
Q2) Find the domain and range of f(x)=√x+[x].
Q3) Find the domain and range of f (x)=√x-[x].
Q4) Find the domain and range of f(x)=1/√x+[x].
Q5) Find the domain and range of f(x)=1/√x-[x].
Q5) Find the domain and range of f(x)=1-|x-2|.
Please answer correct answer.
I will follow the one who gives the most appropriate answer.​

Answer 1

Answer:

Q3)We know that element inside the square root should be greater than or equal to zero .

But in this case since square root is in denominator it can't be equal to zero .

So in this case element inside the square root should be greater than zero .

i.e |x| - x > 0

Now here arises two cases x>0 and x<0

1st case x>0

In this case |x| = x

Therefore equation becomes x - x > 0

=> 0 > 0 Now this is an absurd result or we can say x can't lie in this range

2nd case x<0

In this case |x| = -x ( because x is negative and multiplying it with -1 will make it positive)

So the equation becomes - x - x > 0

=> - 2x > 0 => x < 0

Hence all value less than zero satisfies the equation .

Now we have to take union of the two cases which results in x<0

Thus x can be anything from - infinity to 0 but not 0

Thus domain of function is (- infinity , 0) , 0 is excluded .