Question -
Answer -
(i)┬аGiven,
f(x) = тАУ|x|,┬аx┬атИИ┬аR
We know that,
As┬аf(x)is defined for┬аx┬атИИ┬аR, the domain of┬аf┬аis┬аR.
It is also seen thatthe range of┬аf(x) = тАУ|x| is all real numbers exceptpositive real numbers.
Therefore, the rangeof┬аf┬аis given by (тАУтИЮ, 0].
(ii)┬аf(x) = тИЪ(9 тАУx2)
As тИЪ(9 тАУ x2)┬аisdefined for all real numbers that are greater than or equal to тАУ3 and less thanor equal to 3, for 9 тАУ x2┬атЙе 0.
So, the domainof┬аf(x) is {x: тАУ3 тЙд┬аx┬атЙд 3} or [тАУ3,3].
Now,
For any value of┬аx┬аinthe range [тАУ3, 3], the value of┬аf(x) will lie between 0 and3.
Therefore, the rangeof┬аf(x) is {x: 0 тЙд┬аx┬атЙд 3} or [0, 3].