Question

What is the domain and range of `h(x)=(x-1)/(x^3-9x)`?

Answer 1

Domain: `x in (-oo,-3)uu(-3,0)uu(0,3)uu(3,oo)`
Range : `h(x) in RR or (-oo,oo)`

Explanation:

`h(x)=(x-1)/(x^3-9 x) or h(x)=(x-1)/(x(x^2-9)` or

`h (x)=(x-1)/(x(x+3)(x-3)`

Domain: Possible input value of `x` , if denominator is

zero , the function is undefined .

Domain: `x` is any real value except `x=0 , x =-3 and x=3` .

In interval notation:

`x in (-oo,-3)uu(-3,0)uu(0,3)uu(3,oo)`

Range: Possible output of `h(x)` .When `x=1 ; h(x)=0`

Range : Any real value of `h(x) :. h(x) in RR or (-oo,oo)`

graph{(x-1)/(x^3-9x) [-10, 10, -5, 5]}[Ans]