Determine the domain of the function fx Squareroot x2 4x3

Determine the domain of the function f(x) = Squareroot x^2 - 4/x^3 - 4x. {x 2} {x|x notequalto 0, x notequalto plusminus 2} {x|-2

Solution

2)

The domain of a function is the set of numbers that can go in to a given function. In other words, it is the set of x-values that you can put in to any given equation.

When finding the domain, remember:

Here f(x)=

So by definition denominator cannot be zero.

So the value of x for which the denominator equals zero are, x=0,2,-2

Also the number under a square root must be positive, so x²- 4 should be always greater than zero.

x² – 4 > 0

x² – 4 + 4> +4

x²> 4

x > ±2

so -2 < x < 2

A)

{x< -2} U {x>2}

DOMAIN = (-,-3] U [3,)

B)

{x|x0,x ± 2}

DOMAIN = (-,-3] U [3,)

C)

{x|-2 < x < 2}

DOMAIN = (null set)

Since no elements can in the given region can give a proper definition to f(x).

D)

{x -2} U {x 2}

DOMAIN = (-,-3] U [3,)