Question

Domain of f(x)=√x^(2)+x-6/x^(2)-4

Answer 1

Answer:

Domain is (−∞,−2[∪]3,+∞)

Range is [0,+∞)

Explanation:

Since under square root the polynomial must be positive, the domain is obtained by solving:

x2−x−6≥0

you can obtain the zeroes of the polynomial by solving the associated equation:

x2−x−6=0

x=1±√1−4⋅(−6)2

x=1+√252

x=1±52

x=−2andx=3

so the disequation is solved in the external intervals:

x<−2andx>3

the the domain is:

(−∞,−2[∪]3,+∞)

Since f(x) is positive, due to the result of square root, the range includes all positive real numbers: x≥0