find the domain of the function f(x)=4/x^2-1

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embizze eNotes educator| Certified Educator

Find the domain of `f(x)=4/(x^2-1)` :

The domain of a function is the set of all possible inputs. Generally, you are only concerned with avoiding dividing by zero, taking even roots of negative numbers in the reals, or taking logarithms of negative numbers.

Here, f(x) is a rational function comprised of the ratio of two polynomials. The only possible restrictions to the domain are x's that result in a division by zero.

Factor the denominator:



We see that when x = 1 or -1 we would be dividing by zero, which is undefined.

Thus the domain is all real numbers except 1 and -1.

`D=RR-{1,-1},D=(-oo,-1)uu(-1,1)uu(1,oo)` or `D={x|x!=1,x!=-1}`