Question

find the domain and range of
f(x) = x³-a³/x-a​

Answer 1

f(x)= (x−1)(3−x]

Now,

Under square root the polynomial must be positive. The domain is obtained by solving:-

(x−1)(3−x)≥0

You can obtain the zeroes of the polynomial

(x−1)(3−x)=0

If

x−1=0

x=1

If

3−x=0

⇒x=3

So,

x=1,3

So the polynomial is solved in the external intervals.

x>1,x>3

So,

x∈(1,+∞)