Question

Find the domain and range of function f(x) = √x-5/√3-x​

Answer 1

From the above equation

X-5 cannot be negative therefore x =>5

Also

X-3 cannot be negative and zero ( since in denominator )

Therefore x > 3

From both cases we conclude so such range exist

But there is a third case in which both numerotor and denominator is zero and both are negative

i.e (3,5]

Therefore domain is (3,5]

And range will be put [0, infinity)

You will get the range by putting 3 and 5 in the equation