Find the domain of the function:f (x) = x2 + 4x + 1 x2 − 3x + 2 .
x2 − 3x + 2 = x2 − 2x − x + 2 (Breaking the middle term) = x (x − 2) − (x − 2) = (x − 2)(x − 1) f (x) = x2 + 4x + 1 (x − 1)(x − 2) The above factors of the denominator suggest that f (x) cannot have values of x as 1 or 2. As, in such case, the function itself becomes undefined. Domain of the given function is R − {1, 2} , i.e. all real numbers except 1 and 2.